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 Author ID: ismail.mourad-el-houssieny Published as: Ismail, Mourad E. H.; Ismail, M. E. H.; Ismail, Mourad El-Houssieny; Ismail, Mourad; Ismail, Mourad E.-H.; Ismail, Mourad E.; Mourad, El-Houssieny Ismail; Ismail, M. E.; Ismail, M. H. more...less Homepage: http://math.cos.ucf.edu//~ismail/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef
 Documents Indexed: 307 Publications since 1973, including 3 Books 11 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 123 Co-Authors with 257 Joint Publications 2,407 Co-Co-Authors
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Co-Authors

 58 single-authored 22 Stanton, Dennis W. 17 Simeonov, Plamen C. 17 Zhang, Ruiming 15 Chen, Yang 15 Masson, David R. 14 Rahman, Mizan 11 Askey, Richard Allen 10 Koelink, Erik 9 Bustoz, Joaquin jun. 9 Valent, Galliano 8 Muldoon, Martin E. 7 Al-Salam, Waleed A. 7 Letessier, Jean 6 Li, Xin 5 Dai, Dan 5 Van Assche, Walter 5 Wang, Xiangsheng 5 Wimp, Jet 4 Charris Castañeda, Jairo Alberto 4 Mansour, Zeinab S. I. 4 Muttalib, K. A. 4 Suslov, Sergei K. 4 Zeng, Jiang 3 Chiang, Yik-Man 3 Clark, W. Edwin 3 Fields, Jerry Leon 3 Genest, Vincent X. 3 Grinshpan, Arcadii Z. 3 Gupta, Dharma P. 3 Saad, Nasser 3 Vinet, Luc 3 Zhedanov, Alexei S. 2 Alhaidari, Abdulaziz D. 2 Annaby, Mahmoud H. 2 Ashour, Ola A. 2 Berg, Christian 2 Brown, B. Malcolm 2 Chen, Li-Chen 2 Chihara, Theodore Seio 2 Cohl, Howard Saul 2 Dimitrov, Dimitar K. 2 Gasper, George Jun 2 Ihrig, Edwin C. 2 Kelker, Douglas H. 2 Koornwinder, Tom H. 2 Laforgia, Andrea 2 May, C. Ping 2 Nevai, Paul G. 2 Rashed, Thanaa M. T. 2 Román, Pablo Manuel 2 Sri Ranga, Alagacone 2 Zayed, Ahmed I. 1 Abu Risha, M. H. 1 Ahmed, A. N. 1 Al-Salam, Nadhla A. 1 Ali, Syed Twareque 1 Aslan, Hatice 1 Bahlouli, Hocine 1 Bank, Edward 1 Baricz, Árpád 1 Batir, Necdet 1 Bhatnagar, Gaurav 1 Bressoud, David M. 1 Carteret, Hilary A. 1 Christiansen, Jacob Stordal 1 Dunkl, Charles F. 1 Durán, Antonio José 1 El Ayadi, Moataz M. H. 1 El-Guindy, Ahmad 1 Evans, Ronald J. 1 Evans, William Desmond 1 Garrett, Kristina C. 1 Garvan, Frank G. 1 Ghaleb, Ahmed Fouad 1 Gillis, Joseph E. 1 Gishe, Jemal 1 Gosper, R. William jun. 1 Griffin, James C. 1 Groenevelt, Wolter G. M. 1 Guo, Senlin 1 Jing, Naihuan 1 Johnston, Sarah Jane 1 Kasraoui, Anisse 1 Kim, Dongsu 1 Law, Chun-Kong 1 Libis, Carl A. 1 Lorch, Lee 1 Ma, Jifeng 1 Ma, Wen-Xiu 1 Maitre, Emmanuel 1 Mansour, Zeinab Sayed 1 Merkes, Edward P. 1 Metivet, Thibaut 1 Miller, Kenneth S. 1 Milligan, David L. 1 Monsalve, Sergio 1 Mulla, Fuad S. 1 Nashed, M. Zuhair 1 Nicopoulos, V. Nikos 1 Nikolova, Inna ...and 28 more Co-Authors
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Serials

 23 Journal of Mathematical Analysis and Applications 22 Proceedings of the American Mathematical Society 17 Canadian Journal of Mathematics 17 Advances in Applied Mathematics 17 SIAM Journal on Mathematical Analysis 15 Journal of Approximation Theory 14 Journal of Computational and Applied Mathematics 11 Pacific Journal of Mathematics 11 Transactions of the American Mathematical Society 9 Constructive Approximation 9 Analysis and Applications (Singapore) 7 Journal of Physics A: Mathematical and General 5 Advances in Mathematics 5 Comptes Rendus Mathématiques de l’Académie des Sciences 4 Illinois Journal of Mathematics 4 The Ramanujan Journal 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Applicable Analysis 3 Journal of Mathematical Physics 3 Rocky Mountain Journal of Mathematics 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of Combinatorial Theory. Series A 3 Studies in Applied Mathematics 3 Zeitschrift für Analysis und ihre Anwendungen 3 Methods and Applications of Analysis 3 Annals of Combinatorics 3 Journal of Physics A: Mathematical and Theoretical 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Mathematics of Computation 2 Ars Combinatoria 2 IMRN. International Mathematics Research Notices 2 Journal of Difference Equations and Applications 2 Fractional Calculus & Applied Analysis 2 Contemporary Mathematics 2 Encyclopedia of Mathematics and Its Applications 2 Developments in Mathematics 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 Journal of Computational Physics 1 The Mathematical Intelligencer 1 The Annals of Probability 1 Biometrical Journal 1 The Fibonacci Quarterly 1 Indian Journal of Mathematics 1 Journal of Functional Analysis 1 Mathematica Japonica 1 Mathématica – Revue d’Analyse Numérique et de Théorie de l’Approximation. Mathématica 1 Mathematica Scandinavica 1 Memoirs of the American Mathematical Society 1 Numerical Functional Analysis and Optimization 1 Results in Mathematics 1 European Journal of Combinatorics 1 Complex Variables. Theory and Application 1 Applied Numerical Mathematics 1 Differential and Integral Equations 1 Buletinul Institutului Politehnic din Iași. Secția I 1 Linear Algebra and its Applications 1 Notices of the American Mathematical Society 1 Journal of the Egyptian Mathematical Society 1 ETNA. Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Integral Transforms and Special Functions 1 Arab Journal of Mathematical Sciences 1 Séminaire Lotharingien de Combinatoire 1 Mathematical Inequalities & Applications 1 Physical Review Letters 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Advances in Difference Equations 1 International Journal of Number Theory 1 Fields Institute Communications 1 London Mathematical Society Lecture Note Series 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Malaysian Journal of Mathematical Sciences 1 IET Communications
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Fields

 271 Special functions (33-XX) 68 Harmonic analysis on Euclidean spaces (42-XX) 40 Combinatorics (05-XX) 30 Functions of a complex variable (30-XX) 24 Difference and functional equations (39-XX) 24 Approximations and expansions (41-XX) 21 Number theory (11-XX) 21 Probability theory and stochastic processes (60-XX) 17 Integral transforms, operational calculus (44-XX) 16 Real functions (26-XX) 13 Ordinary differential equations (34-XX) 11 General and overarching topics; collections (00-XX) 11 Quantum theory (81-XX) 9 Sequences, series, summability (40-XX) 8 History and biography (01-XX) 8 Operator theory (47-XX) 7 Integral equations (45-XX) 7 Numerical analysis (65-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Statistics (62-XX) 3 Fluid mechanics (76-XX) 3 Information and communication theory, circuits (94-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Partial differential equations (35-XX) 2 Functional analysis (46-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

Citations contained in zbMATH Open

267 Publications have been cited 3,677 times in 2,163 Documents Cited by Year
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Zbl 1082.42016
2005
Recurrence relations, continued fractions and orthogonal polynomials. Zbl 0548.33001
1984
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Zbl 1172.42008
2009
The combinatorics of q-Hermite polynomials and the Askey-Wilson integral. Zbl 0642.33006
Ismail, Mourad E. H.; Stanton, Dennis; Viennot, Gérard
1987
A generalization of starlike functions. Zbl 0708.30014
Ismail, Mourad E. H.; Merkes, Edward; Styer, David
1990
The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials. Zbl 0483.33004
1982
Ladder operators and differential equations for orthogonal polynomials. Zbl 0927.33011
Chen, Yang; Ismail, Mourad E. H.
1997
On gamma function inequalities. Zbl 0607.33002
Bustoz, Joaquin; Ismail, Mourad E. H.
1986
Completely monotonic functions associated with the gamma function and its q-analogues. Zbl 0589.33001
Ismail, Mourad E. H.; Lorch, Lee; Muldoon, Martin E.
1986
Completely monotonic functions involving the gamma and $$q$$-gamma functions. Zbl 1085.33001
2006
$$q$$-Hermite polynomials, biorthogonal rational functions, and $$q$$-beta integrals. Zbl 0812.33012
Ismail, M. E. H.; Masson, D. R.
1994
Generalized orthogonality and continued fractions. Zbl 0846.33005
Ismail, Mourad E. H.; Masson, David R.
1995
A generalization of ultraspherical polynomials. Zbl 0532.33006
1983
An electrostatics model for zeros of general orthogonal polynomials. Zbl 1011.33011
2000
Bound on the extreme zeros of orthogonal polynomials. Zbl 0744.33005
Ismail, Mourad E. H.; Li, Xin
1992
The associated Askey-Wilson polynomials. Zbl 0738.33011
Ismail, Mourad E. H.; Rahman, Mizan
1991
$$q$$-difference operators for orthogonal polynomials. Zbl 1185.39005
Ismail, Mourad E. H.; Simeonov, Plamen
2009
On a family of approximation operators. Zbl 0375.41011
Ismail, Mourad E. H.; May, C. Ping
1978
Monotonicity of the zeros of a cross-product of Bessel functions. Zbl 0388.33005
Ismail, Mourad E. H.; Muldoon, Martin E.
1978
Special functions, Stieltjes transforms and infinite divisibility. Zbl 0427.60021
Ismail, Mourad E. H.; Kelker, Douglas H.
1979
Variants of the Rogers-Ramanujan identities. Zbl 0944.33015
Garrett, Kristina; Ismail, Mourad E. H.; Stanton, Dennis
1999
Linear birth and death models and associated Laguerre and Meixner polynomials. Zbl 0656.60092
Ismail, Mourad E. H.; Letessier, Jean; Valent, Galliano
1988
Linear $$q$$-difference equations. Zbl 1143.39009
Abu Risha, M. H.; Annaby, M. H.; Ismail, M. E. H.; Mansour, Z. S.
2007
Change of base in Bailey pairs. Zbl 0980.33013
Bressoud, D.; Ismail, M. E. H.; Stanton, D.
2000
On the Askey-Wilson and Rogers polynomials. Zbl 0649.33005
Ismail, Mourad E. H.; Stanton, Dennis
1988
Diagonalization of certain integral operators. Zbl 0838.33012
Ismail, Mourad E. H.; Zhang, Ruiming
1994
$$q$$-Taylor theorems, polynomial expansions, and interpolation of entire functions. Zbl 1035.30025
Ismail, Mourad E. H.; Stanton, Dennis
2003
Asymptotics of $$q$$-orthogonal polynomials and a $$q$$-Airy function. Zbl 1072.33014
2005
Bounds for the small real and purely imaginary zeros of Bessel and related functions. Zbl 0845.33003
Ismail, Mourad E. H.; Muldoon, Martin E.
1995
Jacobi polynomials from compatibility conditions. Zbl 1057.33004
2005
On the variation with respect to a parameter of zeros of Bessel and q- Bessel functions. Zbl 0651.33007
Ismail, Mourad E. H.; Muldoon, Martin E.
1988
Inequalities and monotonicity properties for gamma and $$q$$-gamma functions. Zbl 0819.33001
Ismail, Mourad E.; Muldoon, Martin E.
1994
A simple proof of Ramanujan’s $$_1\Psi_1$$sum. Zbl 0351.33002
1977
Bessel functions and the infinite divisibility of the Student $$t$$-distribution. Zbl 0369.60023
1977
Analytic properties of complex Hermite polynomials. Zbl 1339.33015
2016
The associated ultraspherical polynomials and their q-analogues. Zbl 0451.33003
Bustoz, Joaquin; Ismail, Mourad E. H.
1982
$$q$$-Hermite polynomials and classical orthogonal polynomials. Zbl 0858.33015
Berg, Christian; Ismail, Mourad E. H.
1996
A discrete approach to monotonicity of zeros of orthogonal polynomials. Zbl 0718.33004
Ismail, Mourad E. H.; Muldoon, Martin E.
1991
On asymptotics of Jacobi polynomials. Zbl 0735.33004
Chen, Li-Chen; Ismail, Mourad E. H.
1991
The Askey-Wilson operator and summation theorems. Zbl 0839.33010
1995
Monotonicity properties of determinants of special functions. Zbl 1117.33004
Ismail, Mourad E. H.; Laforgia, Andrea
2007
Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction. Zbl 0526.33009
Al-Salam, Waleed A.; Ismail, Mourad E. H.
1983
On a generalization of Szasz operators. Zbl 0385.41015
1974
Classical orthogonal polynomials as moments. Zbl 0882.33012
Ismail, Mourad E. H.; Stanton, Dennis
1997
Applications of $$q$$-Taylor theorems. Zbl 1024.33012
Ismail, Mourad E. H.; Stanton, Dennis
2003
Small eigenvalues of large Hankel matrices: The indeterminate case. Zbl 1018.47020
Berg, Christian; Chen, Yang; Ismail, Mourad E. H.
2002
The basic Bessel functions and polynomials. Zbl 0456.33005
1981
q-beta integrals and the q-Hermite polynomials. Zbl 0658.33002
Al-Salam, W. A.; Ismail, Mourad E. H.
1988
On sieved orthogonal polynomials. X: General blocks of recurrence relations. Zbl 0805.33006
Charris, Jairo A.; Ismail, Mourad E. H.; Monsalve, Sergio
1994
Thermodynamic relations of the Hermitian matrix ensembles. Zbl 1042.82550
Chen, Yang; Ismail, Mourad E. H.
1997
On the Hellmann-Feynman theorem and the variation of zeros of certain special functions. Zbl 0684.33004
Ismail, Mourad E. H.; Zhang, Ruiming
1988
Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. I. Zbl 0681.33011
Ismail, Mourad E. H.; Libis, Carl A.
1989
Spectral properties of operators using tridiagonalization. Zbl 1248.33019
2012
Asymptotic and generating relations for the q-Jacobi and //$$4Phi_ 3$$ polynomials. Zbl 0489.33011
Ismail, Mourad E. H.; Wilson, James A.
1982
More on electrostatic models for zeros of orthogonal polynomials. Zbl 0981.42015
2000
On sieved orthogonal polynomials. V: Sieved Pollaczek polynomials. Zbl 0645.33018
Charris, Jairo A.; Ismail, Mourad E. H.
1987
Sieved orthogonal polynomials. VII: Generalized polynomial mappings. Zbl 0790.33007
Charris, Jairo A.; Ismail, Mourad E. H.
1993
Difference equations and quantized discriminants for $$q$$-orthogonal polynomials. Zbl 1032.33012
2003
$$q$$-integral and moment representations for $$q$$-orthogonal polynomials. Zbl 1009.33015
Ismail, Mourad E. H.; Stanton, Dennis
2002
Zeros of entire functions and a problem of Ramanujan. Zbl 1107.33018
Ismail, Mourad E. H.; Zhang, Changgui
2007
Permutation problems and special functions. Zbl 0313.05005
1976
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
2016
The variation of zeros of certain orthogonal polynomials. Zbl 0628.33001
1987
Some indetermining moment problems and Freud-like weights. Zbl 0913.30024
Chen, Yang; Ismail, M. E. H.
1998
Ladder operators for $$q$$-orthogonal polynomials. Zbl 1154.33010
Chen, Yang; Ismail, Mourad E. H.
2008
Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. III: Associated continuous dual $$q$$-Hahn polynomials. Zbl 0878.33011
Gupta, D. P.; Ismail, M. E. H.; Masson, D. R.
1996
The $$q$$-Laguerre polynomials and related moment problems. Zbl 0893.33009
Ismail, Mourad E. H.; Rahman, Mizan
1998
A queueing model and a set of orthogonal polynomials. Zbl 0579.60093
1985
The Askey-Wilson polynomials and $$q$$-Sturm-Liouville problems. Zbl 0860.33012
Brown, B. Malcolm; Evans, W. Desmond; Ismail, Mourad E. H.
1996
Integral representations and complete monotonicity of various quotients of Bessel functions. Zbl 0343.33005
1977
Quadratic birth and death processes and associated continuous dual Hahn polynomials. Zbl 0692.33009
Ismail, Mourad E. H.; Letessier, Jean; Valent, Galliano
1989
Two families of associated Wilson polynomials. Zbl 0712.33005
Ismail, M. E. H.; Letessier, J.; Valent, G.; Wimp, J.
1990
Some combinatorial and analytical identities. Zbl 1256.05021
Ismail, Mourad E. H.; Stanton, Dennis
2012
Inequalities involving gamma and psi functions. Zbl 1042.33002
Clark, W. Edwin; Ismail, Mourad E. H.
2003
The $$J$$-matrix method. Zbl 1216.33020
2011
On sieved orthogonal polynomials. IX: Orthogonality on the unit circle. Zbl 0771.33007
Ismail, Mourad E. H.; Li, Xin
1992
Relation between polynomials orthogonal on the unit circle with respect to different weights. Zbl 0752.33004
Ismail, Mourad E. H.; Ruedemann, Richard W.
1992
The Dunkl oscillator in the plane. Part I: Superintegrability, separated wavefunctions and overlap coefficients. Zbl 1267.81139
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
2013
Three routes to the exact asymptotics for the one-dimensional quantum walk. Zbl 1049.82025
Carteret, Hilary A.; Ismail, Mourad E. H.; Richmond, Bruce
2003
Quantum mechanics without potential function. Zbl 1330.81105
Alhaidari, A. D.; Ismail, M. E. H.
2015
Discriminants and functional equations for polynomials orthogonal on the unit circle. Zbl 0982.33004
Ismail, Mourad E. H.; Witte, Nicholas S.
2001
On the positivity of some $$_1F_2$$’s. Zbl 0301.33002
Fields, Jerry L.; Ismail, Mourad El-Houssieny
1975
Difference equations and discriminants for discrete orthogonal polynomials. Zbl 1081.33014
Ismail, Mourad E. H.; Nikolova, Inna; Simeonov, Plamen
2004
The attractive Coulomb potential polynomials. Zbl 0584.42016
Bank, Edward; Ismail, Mourad E. H.
1985
On sieved orthogonal polynomials. III: Orthogonality on several intervals. Zbl 0612.33009
1986
On some strange summation formulas. Zbl 0793.33016
Gosper, R. William; Ismail, Mourad E. H.; Zhang, Ruiming
1993
A $$q$$-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem. Zbl 1053.33002
Ismail, Mourad E.; Zayed, Ahmed I.
2003
Discriminants and functions of the second kind of orthogonal polynomials. Zbl 0911.42012
1998
On differential equations for orthogonal polynomials. Zbl 0932.33007
Ismail, Mourad E. H.; Wimp, Jet
1998
Complete monotonicity of modified Bessel functions. Zbl 0685.33004
1990
Determinants with orthogonal polynomial entries. Zbl 1083.15011
2005
On sieved orthogonal polynomials. I: Symmetric Pollaczek analogues. Zbl 0576.33005
1985
Extremal measures for a system of orthogonal polynomials. Zbl 0783.33007
Chihara, Theodore S.; Ismail, Mourad E. H.
1993
Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials. Zbl 1259.05022
Ismail, Mourad E. H.; Kasraoui, Anisse; Zeng, Jiang
2013
On sampling theory and basic Sturm-Liouville systems. Zbl 1128.39014
Annaby, M. H.; Bustoz, J.; Ismail, M. E. H.
2007
Strong asymptotics for Krawtchouk polynomials. Zbl 0948.41018
Ismail, Mourad E. H.; Simeonov, Plamen
1998
Zeros of combinations of Bessel functions and their derivatives. Zbl 0659.33003
Ismail, M. E. H.; Muldoon, M. E.
1988
More orthogonal polynomials as moments. Zbl 0905.05083
Ismail, Mourad E. H.; Stanton, Dennis
1998
Spectral analysis of certain Schrödinger operators. Zbl 1270.30003
2012
Diagonalization of certain integral operators. II. Zbl 0868.33015
Ismail, Mourad E. H.; Rahman, Mizan; Zhang, Ruiming
1996
The asymptotic iteration method revisited. Zbl 1443.34021
2020
Encyclopedia of special functions: the Askey-Bateman project. Volume 1. Univariate orthogonal polynomials. With the assistance by Walter van Assche. Zbl 1466.33001
2020
A necessary and sufficient condition for sequences to be minimal completely monotonic. Zbl 1487.26016
Wang, Xi-Feng; Ismail, Mourad E. H.; Batir, Necdet; Guo, S.
2020
A discrete and $$q$$ asymptotic iteration method. Zbl 1454.39010
2020
$$R_{II}$$ type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle. Zbl 1405.33017
Ismail, M. E. H.; Ranga, A. Sri
2019
Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice. Zbl 1431.33011
2019
Doubly infinite Jacobi matrices revisited: resolvent and spectral measure. Zbl 07003588
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng
2019
On quasi-orthogonal polynomials: their differential equations, discriminants and electrostatics. Zbl 1479.33008
Ismail, Mourad E. H.; Wang, Xiang-Sheng
2019
$$q$$-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials. Zbl 1423.05029
Ismail, Mourad E. H.; Mansour, Zeinab S. I.
2019
Asymptotics of partition functions in a fermionic matrix model and of related $$q$$-polynomials. Zbl 1419.81028
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng
2019
Integral and series representations of $$q$$-polynomials and functions. I. Zbl 1387.33022
Ismail, Mourad E. H.; Zhang, Ruiming
2018
$$q$$-Bessel functions and Rogers-Ramanujan type identities. Zbl 1409.11082
Ismail, Mourad E. H.; Zhang, Ruiming
2018
Generalized Burchnall-type identities for orthogonal polynomials and expansions. Zbl 1393.33013
2018
On some $$2D$$ orthogonal $$q$$-polynomials. Zbl 1380.33004
Ismail, Mourad E. H.; Zhang, Ruiming
2017
A review of multivariate orthogonal polynomials. Zbl 1371.33025
Ismail, Mourad E. H.; Zhang, Ruiming
2017
Diophantine properties of orthogonal polynomials and rational functions. Zbl 1362.33012
Ismail, Mourad E. H.; Rahman, Mizan
2017
Integral and series representations of $$q$$-polynomials and functions. II: Schur polynomials and the Rogers-Ramanujan identities. Zbl 1380.33010
Ismail, Mourad E. H.; Zhang, Ruiming
2017
Inequalities for gamma and $$q$$-gamma functions of complex arguments. Zbl 1371.33004
2017
Combinatorial and analytic properties of the $$n$$-dimensional Hermite polynomials. Zbl 1366.33012
Ismail, Mourad E. H.; Simeonov, Plamen
2017
Analytic properties of complex Hermite polynomials. Zbl 1339.33015
2016
Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
2016
Classes of bivariate orthogonal polynomials. Zbl 1333.33019
Ismail, Mourad E. H.; Zhang, Ruiming
2016
Kibble-Slepian formula and generating functions for 2D polynomials. Zbl 1347.33022
Ismail, Mourad E. H.; Zhang, Ruiming
2016
Formulas and identities involving the Askey-Wilson operator. Zbl 1336.33026
Ismail, Mourad E. H.; Simeonov, Plamen
2016
Quantum mechanics without potential function. Zbl 1330.81105
Alhaidari, A. D.; Ismail, M. E. H.
2015
Complex Hermite polynomials: their combinatorics and integral operators. Zbl 1308.05009
Ismail, Mourad E. H.; Simeonov, Plamen
2015
A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials. Zbl 1305.33026
Ismail, Mourad E. H.; Zeng, Jiang
2015
Two variable extensions of the Laguerre and disc polynomials. Zbl 1309.33015
Ismail, Mourad E. H.; Zeng, Jiang
2015
Expansions in the Askey-Wilson polynomials. Zbl 1309.33020
Ismail, Mourad E. H.; Stanton, Dennis
2015
On certain dual $$q$$-integral equations. Zbl 1316.45004
Ashour, Ola A.; Ismail, Mourad E. H.; Mansour, Zeinab S.
2015
Asymptotics for Laguerre polynomials with large order and parameters. Zbl 1315.33013
Dai, Dan; Ismail, Mourad E. H.; Wang, Jun
2015
Landau constants and their $$q$$-analogues. Zbl 1312.41041
Ismail, Mourad E. H.; Li, Xin; Rahman, M.
2015
Heine representations and monotonicity properties of determinants and Pfaffians. Zbl 1346.15005
Ismail, Mourad E. H.; Simeonov, Plamen
2015
The Dunkl oscillator in the plane. II: Representations of the symmetry algebra. Zbl 1292.81041
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
2014
Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. Zbl 1315.41014
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng
2014
Functions of the second kind for classical polynomials. Zbl 1285.33013
Ismail, Mourad E. H.; Mansour, Zeinab S. I.
2014
The Dunkl oscillator in the plane. Part I: Superintegrability, separated wavefunctions and overlap coefficients. Zbl 1267.81139
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
2013
Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials. Zbl 1259.05022
Ismail, Mourad E. H.; Kasraoui, Anisse; Zeng, Jiang
2013
Turán type inequalities for Tricomi confluent hypergeometric functions. Zbl 1273.33006
Baricz, Árpád; Ismail, Mourad E. H.
2013
A class of hypergeometric polynomials with zeros on the unit circle: extremal and orthogonal properties and quadrature formulas. Zbl 1268.33007
Dimitrov, D. K.; Ismail, M. E. H.; Sri Ranga, A.
2013
Spectral decomposition and matrix-valued orthogonal polynomials. Zbl 1286.42035
2013
Interlacing of zeros of orthogonal polynomials under modification of the measure. Zbl 1337.30003
Dimitrov, Dimitar K.; Ismail, Mourad E. H.; Rafaeli, Fernando R.
2013
Asymptotics of generalized derangements. Zbl 1270.33004
Ismail, Mourad E. H.; Simeonov, Plamen
2013
Plancherel-Rotach asymptotics for $$q$$-orthogonal polynomials. Zbl 1272.33019
Ismail, Mourad E. H.; Li, Xin
2013
Spectral properties of operators using tridiagonalization. Zbl 1248.33019
2012
Some combinatorial and analytical identities. Zbl 1256.05021
Ismail, Mourad E. H.; Stanton, Dennis
2012
Spectral analysis of certain Schrödinger operators. Zbl 1270.30003
2012
Some orthogonal polynomials arising from coherent states. Zbl 1245.81052
Ali, S. Twareque; Ismail, Mourad E. H.
2012
The Dirac-Coulomb problem: a mathematical revisit. Zbl 1255.81131
Alhaidari, A. D.; Bahlouli, H.; Ismail, M. E. H.
2012
Connection relations and characterizations of orthogonal polynomials. Zbl 1248.33033
Ismail, Mourad E. H.; Simeonov, Plamen
2012
The $$J$$-matrix method. Zbl 1216.33020
2011
Connection relations and expansions. Zbl 1235.05020
Ismail, Mourad E. H.; Rahman, Mizan
2011
Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials. Zbl 1215.39007
Ismail, Mourad E. H.; Simeonov, Plamen
2011
Equations of motion for zeros of orthogonal polynomials related to the Toda lattices. Zbl 1216.33024
Ismail, Mourad E. H.; Ma, Wen-Xiu
2011
Structure relations for $$q$$-polynomials and some applications. Zbl 1216.33039
Ismail, Mourad E. H.; Johnston, Sarah Jane; Mansour, Zeinab Sayed
2011
On a family of positive linear integral operators. Zbl 1248.41026
2011
Characterizations of continuous and discrete $$q$$-ultraspherical polynomials. Zbl 1214.33010
Ismail, Mourad E. H.; Obermaier, Josef
2011
Orthogonal polynomials, their recursions, and functional equations. Zbl 1234.33013
2011
Hypergeometric origins of Diophantine properties associated with the Askey scheme. Zbl 1193.33016
Chen, Yang; Ismail, Mourad E. H.
2010
$$q$$-analogues of Freud weights and nonlinear difference equations. Zbl 1211.39007
Ismail, Mourad E. H.; Mansour, Z. S. I.
2010
Addition theorems via continued fractions. Zbl 1194.33017
Ismail, Mourad E. H.; Zeng, Jiang
2010
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Zbl 1172.42008
2009
$$q$$-difference operators for orthogonal polynomials. Zbl 1185.39005
Ismail, Mourad E. H.; Simeonov, Plamen
2009
One parameter generalizations of the Fibonacci and Lucas numbers. Zbl 1234.11016
2009
Structure relations for orthogonal polynomials. Zbl 1166.42014
2009
Ladder operators for $$q$$-orthogonal polynomials. Zbl 1154.33010
Chen, Yang; Ismail, Mourad E. H.
2008
Resultants of Chebyshev polynomials. Zbl 1194.12001
Gishe, Jemal; Ismail, Mourad E. H.
2008
Linear $$q$$-difference equations. Zbl 1143.39009
Abu Risha, M. H.; Annaby, M. H.; Ismail, M. E. H.; Mansour, Z. S.
2007
Monotonicity properties of determinants of special functions. Zbl 1117.33004
Ismail, Mourad E. H.; Laforgia, Andrea
2007
Zeros of entire functions and a problem of Ramanujan. Zbl 1107.33018
Ismail, Mourad E. H.; Zhang, Changgui
2007
On sampling theory and basic Sturm-Liouville systems. Zbl 1128.39014
Annaby, M. H.; Bustoz, J.; Ismail, M. E. H.
2007
Scaled asymptotics for $$q$$-orthogonal polynomials. Zbl 1110.33011
Ismail, Mourad E. H.; Zhang, Ruiming
2007
Generalizations of Chebyshev polynomials and polynomial mappings. Zbl 1176.33011
Chen, Yang; Griffin, James; Ismail, Mourad E. H.
2007
Inequalities and asymptotics for a terminating $${}_4F_3$$ series. Zbl 1156.33002
Ismail, Mourad E. H.; Simeonov, Plamen
2007
Completely monotonic functions involving the gamma and $$q$$-gamma functions. Zbl 1085.33001
2006
A moment problem and a family of integral evaluations. Zbl 1089.33016
Christiansen, Jacob S.; Ismail, Mourad E. H.
2006
Chaotic and periodic asymptotics for $$q$$-orthogonal polynomials. Zbl 1109.33025
Ismail, Mourad E. H.; Zhang, Ruiming
2006
On value distribution theory of second order periodic ODEs, special functions and orthogonal polynomials. Zbl 1115.34081
Chiang, Yik-Man; Ismail, Mourad E. H.
2006
Functional inequalities for incomplete gamma and related functions. Zbl 1098.33001
Ismail, Mourad E. H.; Laforgia, Andrea
2006
Differential coefficients of orthogonal matrix polynomials. Zbl 1100.42017
Duran, Antonio J.; Ismail, Mourad E. H.
2006
On formulas of Ramanujan and Evans. Zbl 1106.33005
2006
Orthogonal polynomials and Ramanujan’s $$q$$-continued fractions. Zbl 1107.33010
Ismail, Mourad E. H.; Li, Xin
2006
Ramanujan continued fractions via orthogonal polynomials. Zbl 1103.11003
Ismail, Mourad E. H.; Stanton, Dennis
2006
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Zbl 1082.42016
2005
Asymptotics of $$q$$-orthogonal polynomials and a $$q$$-Airy function. Zbl 1072.33014
2005
Jacobi polynomials from compatibility conditions. Zbl 1057.33004
2005
Determinants with orthogonal polynomial entries. Zbl 1083.15011
2005
New proofs of some $$q$$ -series results. Zbl 1219.33019
Ismail, Mourad E. H.; Zhang, Ruiming
2005
Theory and applications of special functions. A volume dedicated to Mizan Rahman. Papers from the special session of the American Mathematical Society annual meeting held in Baltimore, MD, USA, January 15–18, 2003. Zbl 1124.33001
2005
Difference equations and discriminants for discrete orthogonal polynomials. Zbl 1081.33014
Ismail, Mourad E. H.; Nikolova, Inna; Simeonov, Plamen
2004
$$q$$-Taylor theorems, polynomial expansions, and interpolation of entire functions. Zbl 1035.30025
Ismail, Mourad E. H.; Stanton, Dennis
2003
Applications of $$q$$-Taylor theorems. Zbl 1024.33012
Ismail, Mourad E. H.; Stanton, Dennis
2003
Difference equations and quantized discriminants for $$q$$-orthogonal polynomials. Zbl 1032.33012
2003
Inequalities involving gamma and psi functions. Zbl 1042.33002
Clark, W. Edwin; Ismail, Mourad E. H.
2003
Three routes to the exact asymptotics for the one-dimensional quantum walk. Zbl 1049.82025
Carteret, Hilary A.; Ismail, Mourad E. H.; Richmond, Bruce
2003
A $$q$$-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem. Zbl 1053.33002
Ismail, Mourad E.; Zayed, Ahmed I.
2003
A generalization of a theorem of Bochner. Zbl 1043.33009
2003
Remarks on ”Differential equation of Appell polynomials…”. Zbl 1033.33006
2003
Tribasic integrals and identities of Rogers-Ramanujan type. Zbl 1033.33012
Ismail, M. E. H.; Stanton, D.
2003
Application of upper and lower bounds for the domination number to Vizing’s conjecture. Zbl 1072.05537
Clark, W. Edwin; Ismail, Mourad E. H.; Suen, Stephen
2003
...and 167 more Documents
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Cited by 1,890 Authors

 140 Ismail, Mourad El-Houssieny 41 Zhedanov, Alexei S. 39 Srivastava, Hari Mohan 38 Baricz, Árpád 37 Vinet, Luc 33 Marcellán Español, Francisco 32 Van Assche, Walter 26 Qi, Feng 24 Chen, Yang 24 Sri Ranga, Alagacone 24 Zhang, Ruiming 23 Koelink, Erik 21 Cao, Jian 20 Area, Iván 20 Tariboon, Jessada 19 Stanton, Dennis W. 19 Yang, Zhenhang 18 Ntouyas, Sotiris K. 18 Rahman, Mizan 17 Castillo, Kenier 17 Dimitrov, Dimitar K. 17 Wong, Roderick Sue-Chuen 17 Zeng, Jiang 16 Alhaidari, Abdulaziz D. 16 Filipuk, Galina V. 16 Jordaan, Kerstin 16 Khan, Bilal 16 Khan, Nazar 16 Szabłowski, Paweł Jerzy 15 Godoy, Eduardo Paciência 14 Berg, Christian 14 Simeonov, Plamen C. 13 Ahmad, Qazi Zahoor 13 Alzer, Horst 13 Bouzeffour, Fethi 13 Karp, Dmitriĭ Borisovich 12 Bryc, Włodzimierz 12 Chu, Wenchang 12 Martínez-Finkelshtein, Andrei 12 Muldoon, Martin E. 12 Petronilho, José C. 11 Annaby, Mahmoud H. 11 Atakishiev, Natig M. 11 Darus, Maslina 11 Guo, Bai-Ni 11 Gupta, Vijay 11 Wang, Xiangsheng 10 Abreu, Luís Daniel 10 Ahmad, Bashir 10 Bracciali, Cleonice Fátima 10 Dominici, Diego Ernesto 10 Genest, Vincent X. 10 Koepf, Wolfram A. 10 Zhu, Mengkun 9 Chu, Yuming 9 Driver, Kathy A. 9 Fitouhi, Ahmed 9 Forrester, Peter J. 9 Foupouagnigni, Mama 9 Ghanmi, Allal 9 Mansour, Zeinab S. I. 9 Ronveaux, André 9 Štampach, František 9 Suslov, Sergei K. 9 Tsujimoto, Satoshi 9 Zhao, Yuqiu 8 Branquinho, Amílcar José Pinto Lopes 8 Dai, Dan 8 Dehesa, Jesús S. 8 Griffin, James C. 8 Grünbaum, Francisco Alberto 8 Mouayn, Zouhaïr 8 Nevai, Paul G. 8 Tian, Jingfeng 8 Valent, Galliano 8 Zhang, Lun 7 Çetinkaya, Asena 7 Chen, William Yong-Chuan 7 Chihara, Theodore Seio 7 Grinshpan, Arcadii Z. 7 Hussain, Saqib 7 Khan, Shahid Ali 7 Krasikov, Ilia 7 Laforgia, Andrea 7 Liu, Zhi-Guo 7 Masjed-Jamei, Mohammad 7 Masson, David R. 7 Mehrez, Khaled 7 Pogány, Tibor K. 7 Rebocho, M. N. 7 Saad, Nasser 7 Salem, Ahmed 7 Sasaki, Ryu 7 Singh, Sanjeev-Kumar 7 Szwarc, Ryszard 7 van Diejen, Jan Felipe 7 Warnaar, S. Ole 7 Zhang, Zhizheng 6 Agrawal, Purshottam Narain 6 Aktaş, İbrahim ...and 1,790 more Authors
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Cited in 343 Serials

 178 Journal of Mathematical Analysis and Applications 140 Journal of Approximation Theory 120 Journal of Computational and Applied Mathematics 113 Proceedings of the American Mathematical Society 93 The Ramanujan Journal 77 Journal of Mathematical Physics 48 Integral Transforms and Special Functions 46 Advances in Applied Mathematics 43 Applied Mathematics and Computation 38 Advances in Difference Equations 36 Transactions of the American Mathematical Society 36 Journal of Difference Equations and Applications 35 Constructive Approximation 25 Advances in Mathematics 24 Journal of Combinatorial Theory. Series A 22 Journal of Inequalities and Applications 22 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 21 Communications in Mathematical Physics 21 Rocky Mountain Journal of Mathematics 21 Results in Mathematics 20 AIMS Mathematics 19 Linear Algebra and its Applications 17 Discrete Mathematics 17 Analysis and Applications (Singapore) 15 Mathematics of Computation 15 Numerical Algorithms 14 Filomat 14 Abstract and Applied Analysis 14 Random Matrices: Theory and Applications 13 Journal of Statistical Physics 13 Journal of Functional Analysis 12 Journal of Function Spaces 11 Computers & Mathematics with Applications 11 Turkish Journal of Mathematics 11 Computational Methods and Function Theory 10 Letters in Mathematical Physics 10 Studies in Applied Mathematics 10 Statistics & Probability Letters 10 Indagationes Mathematicae. New Series 10 Infinite Dimensional Analysis, Quantum Probability and Related Topics 10 Journal of High Energy Physics 10 International Journal of Number Theory 10 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 9 Theoretical and Mathematical Physics 9 Duke Mathematical Journal 9 European Journal of Combinatorics 9 Acta Applicandae Mathematicae 9 Mediterranean Journal of Mathematics 9 Complex Analysis and Operator Theory 8 Applied Numerical Mathematics 8 Positivity 8 Afrika Matematika 7 International Journal of Mathematics and Mathematical Sciences 7 Expositiones Mathematicae 7 Mathematical Inequalities & Applications 7 Analysis and Mathematical Physics 6 Applicable Analysis 6 Reports on Mathematical Physics 6 Ukrainian Mathematical Journal 6 The Annals of Probability 6 Numerical Functional Analysis and Optimization 6 Journal of Nonlinear Mathematical Physics 6 Journal of Classical Analysis 5 Analysis Mathematica 5 Bulletin of the Australian Mathematical Society 5 Nuclear Physics. B 5 Monatshefte für Mathematik 5 Probability Theory and Related Fields 5 Applied Mathematics Letters 5 Bulletin des Sciences Mathématiques 5 Advances in Computational Mathematics 5 Arab Journal of Mathematical Sciences 5 Annals of Combinatorics 5 Asian-European Journal of Mathematics 4 Journal d’Analyse Mathématique 4 Mathematical Notes 4 Journal of Number Theory 4 Mathematische Nachrichten 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 Zeitschrift für Analysis und ihre Anwendungen 4 Journal of Symbolic Computation 4 Queueing Systems 4 Aequationes Mathematicae 4 Annals of Physics 4 Stochastic Processes and their Applications 4 Journal of Mathematical Sciences (New York) 4 Computational and Applied Mathematics 4 Séminaire Lotharingien de Combinatoire 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of Statistical Mechanics: Theory and Experiment 4 Boundary Value Problems 4 Palestine Journal of Mathematics 3 Archive for Rational Mechanics and Analysis 3 International Journal of Theoretical Physics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Physics Letters. A 3 Problems of Information Transmission 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Chaos, Solitons and Fractals ...and 243 more Serials
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Cited in 60 Fields

 1,316 Special functions (33-XX) 416 Harmonic analysis on Euclidean spaces (42-XX) 291 Combinatorics (05-XX) 252 Functions of a complex variable (30-XX) 211 Real functions (26-XX) 201 Number theory (11-XX) 197 Difference and functional equations (39-XX) 194 Probability theory and stochastic processes (60-XX) 191 Approximations and expansions (41-XX) 156 Ordinary differential equations (34-XX) 141 Quantum theory (81-XX) 120 Operator theory (47-XX) 116 Linear and multilinear algebra; matrix theory (15-XX) 89 Integral transforms, operational calculus (44-XX) 83 Numerical analysis (65-XX) 67 Partial differential equations (35-XX) 48 Functional analysis (46-XX) 42 Statistical mechanics, structure of matter (82-XX) 41 Nonassociative rings and algebras (17-XX) 41 Statistics (62-XX) 35 Information and communication theory, circuits (94-XX) 32 Dynamical systems and ergodic theory (37-XX) 32 Sequences, series, summability (40-XX) 19 Operations research, mathematical programming (90-XX) 17 Topological groups, Lie groups (22-XX) 16 Field theory and polynomials (12-XX) 16 Integral equations (45-XX) 16 Biology and other natural sciences (92-XX) 15 Computer science (68-XX) 13 Optics, electromagnetic theory (78-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Abstract harmonic analysis (43-XX) 11 Relativity and gravitational theory (83-XX) 10 History and biography (01-XX) 10 Group theory and generalizations (20-XX) 9 Potential theory (31-XX) 7 Algebraic geometry (14-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Commutative algebra (13-XX) 6 Differential geometry (53-XX) 6 Fluid mechanics (76-XX) 5 General and overarching topics; collections (00-XX) 5 Associative rings and algebras (16-XX) 5 Convex and discrete geometry (52-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Measure and integration (28-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Systems theory; control (93-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX)

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