Edit Profile (opens in new tab) Ismail, Mourad El-Houssieny Co-Author Distance 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, E. H. Mourad; Ismail, M. E.; Ismail, M. H. more...less Homepage: https://sciences.ucf.edu/math/person/mourad-ismail/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · dblp · GND · IdRef Documents Indexed: 319 Publications since 1973, including 3 Books and 7 Additional arXiv Preprints 12 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 132 Co-Authors with 271 Joint Publications 2,818 Co-Co-Authors all top 5 Co-Authors 59 single-authored 23 Stanton, Dennis W. 19 Zhang, Ruiming 18 Simeonov, Plamen C. 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 Mansour, Zeinab S. I. 5 Van Assche, Walter 5 Wang, Xiangsheng 5 Wimp, Jet 4 Charris Castañeda, Jairo Alberto 4 Muttalib, K. A. 4 Suslov, Sergei K. 4 Zeng, Jiang 3 Alhaidari, Abdulaziz D. 3 Chiang, Yik-Man 3 Clark, W. Edwin 3 Cohl, Howard Saul 3 Dimitrov, Dimitar K. 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. 3 Zhou, Keru 2 Ali, Syed Twareque 2 Annaby, Mahmoud H. 2 Ashour, Ola A. 2 Berg, Christian 2 Bhatnagar, Gaurav 2 Brown, B. Malcolm 2 Chen, Li-Chen 2 Chihara, Theodore Seio 2 El-Guindy, Ahmad 2 Garvan, Frank G. 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 Al-Salam, Nadhla A. 1 Alladi, Krishnaswami 1 Aslan, Hatice 1 Bahlouli, Hocine 1 Bank, Edward 1 Baricz, Árpád 1 Batir, Necdet 1 Bressoud, David M. 1 Bryc, Włodzimierz 1 Carteret, Hilary A. 1 Christiansen, Jacob Stordal 1 Dunkl, Charles F. 1 Durán, Antonio José 1 El Ayadi, Moataz M. H. 1 Evans, Ronald J. 1 Evans, William Desmond 1 Gadjev, Ivan 1 Garrett, Kristina C. 1 Ghaleb, Ahmed Fouad 1 Gillis, Joseph E. 1 Gishe, Jemal 1 Glasser, M. Lawrence 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 Lefebvre-Lepot, Aline 1 Libis, Carl A. 1 Lin, Shao-Shiung 1 Lorch, Lee 1 Ma, Jifeng 1 Ma, Wen-Xiu 1 Mansour, Zeinab Sayed 1 Merkes, Edward P. 1 Miller, Kenneth S. 1 Milligan, David L. 1 Monsalve, Sergio ...and 34 more Co-Authors all top 5 Serials 23 Journal of Mathematical Analysis and Applications 22 Proceedings of the American Mathematical Society 19 Advances in Applied Mathematics 17 Canadian Journal of 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 10 Analysis and Applications (Singapore) 9 Constructive Approximation 7 Journal of Physics A: Mathematical and General 6 The Ramanujan Journal 5 Advances in Mathematics 5 Comptes Rendus Mathématiques de l’Académie des Sciences 4 Journal of Mathematical Physics 4 Illinois Journal of Mathematics 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Applicable Analysis 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 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 Physica D 1 Applied Numerical Mathematics 1 Differential and Integral Equations 1 Aequationes Mathematicae 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 IET Communications all top 5 Fields 278 Special functions (33-XX) 68 Harmonic analysis on Euclidean spaces (42-XX) 42 Combinatorics (05-XX) 33 Functions of a complex variable (30-XX) 28 Approximations and expansions (41-XX) 26 Difference and functional equations (39-XX) 22 Number theory (11-XX) 21 Probability theory and stochastic processes (60-XX) 19 Real functions (26-XX) 18 Integral transforms, operational calculus (44-XX) 14 Ordinary differential equations (34-XX) 12 General and overarching topics; collections (00-XX) 11 Quantum theory (81-XX) 10 Operator theory (47-XX) 9 History and biography (01-XX) 9 Sequences, series, summability (40-XX) 8 Integral equations (45-XX) 6 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 Optics, electromagnetic theory (78-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 Fluid mechanics (76-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 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 279 Publications have been cited 4,397 times in 2,568 Documents Cited by ▼ Year ▼ Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Zbl 1082.42016 Ismail, Mourad E. H. 482 2005 Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Zbl 1172.42008 Ismail, Mourad E. H. 115 2009 A generalization of starlike functions. Zbl 0708.30014 Ismail, Mourad E. H.; Merkes, Edward; Styer, David 103 1990 Recurrence relations, continued fractions and orthogonal polynomials. Zbl 0548.33001 Askey, Richard; Ismail, Mourad 100 1984 The combinatorics of q-Hermite polynomials and the Askey-Wilson integral. Zbl 0642.33006 Ismail, Mourad E. H.; Stanton, Dennis; Viennot, Gérard 93 1987 The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials. Zbl 0483.33004 Ismail, Mourad E. H. 83 1982 Ladder operators and differential equations for orthogonal polynomials. Zbl 0927.33011 Chen, Yang; Ismail, Mourad E. H. 82 1997 On gamma function inequalities. Zbl 0607.33002 Bustoz, Joaquin; Ismail, Mourad E. H. 73 1986 A generalization of ultraspherical polynomials. Zbl 0532.33006 Askey, R.; Ismail, Mourad E.-H. 62 1983 Generalized orthogonality and continued fractions. Zbl 0846.33005 Ismail, Mourad E. H.; Masson, David R. 59 1995 Completely monotonic functions associated with the gamma function and its q-analogues. Zbl 0589.33001 Ismail, Mourad E. H.; Lorch, Lee; Muldoon, Martin E. 56 1986 Completely monotonic functions involving the gamma and \(q\)-gamma functions. Zbl 1085.33001 Grinshpan, Arcadii Z.; Ismail, Mourad E. H. 54 2006 \(q\)-Hermite polynomials, biorthogonal rational functions, and \(q\)-beta integrals. Zbl 0812.33012 Ismail, M. E. H.; Masson, D. R. 52 1994 An electrostatics model for zeros of general orthogonal polynomials. Zbl 1011.33011 Ismail, Mourad E. H. 51 2000 Bound on the extreme zeros of orthogonal polynomials. Zbl 0744.33005 Ismail, Mourad E. H.; Li, Xin 49 1992 Linear \(q\)-difference equations. Zbl 1143.39009 Abu Risha, M. H.; Annaby, M. H.; Ismail, M. E. H.; Mansour, Z. S. 46 2007 On a family of approximation operators. Zbl 0375.41011 Ismail, Mourad E. H.; May, C. Ping 45 1978 Variants of the Rogers-Ramanujan identities. Zbl 0944.33015 Garrett, Kristina; Ismail, Mourad E. H.; Stanton, Dennis 43 1999 \(q\)-difference operators for orthogonal polynomials. Zbl 1185.39005 Ismail, Mourad E. H.; Simeonov, Plamen 41 2009 The associated Askey-Wilson polynomials. Zbl 0738.33011 Ismail, Mourad E. H.; Rahman, Mizan 41 1991 Change of base in Bailey pairs. Zbl 0980.33013 Bressoud, D.; Ismail, M. E. H.; Stanton, D. 40 2000 A simple proof of Ramanujan’s \(_1\Psi_1\)sum. Zbl 0351.33002 Ismail, Mourad E. H. 40 1977 Special functions, Stieltjes transforms and infinite divisibility. Zbl 0427.60021 Ismail, Mourad E. H.; Kelker, Douglas H. 40 1979 Linear birth and death models and associated Laguerre and Meixner polynomials. Zbl 0656.60092 Ismail, Mourad E. H.; Letessier, Jean; Valent, Galliano 38 1988 Jacobi polynomials from compatibility conditions. Zbl 1057.33004 Chen, Yang; Ismail, Mourad 38 2005 On the Askey-Wilson and Rogers polynomials. Zbl 0649.33005 Ismail, Mourad E. H.; Stanton, Dennis 37 1988 Diagonalization of certain integral operators. Zbl 0838.33012 Ismail, Mourad E. H.; Zhang, Ruiming 37 1994 Monotonicity of the zeros of a cross-product of Bessel functions. Zbl 0388.33005 Ismail, Mourad E. H.; Muldoon, Martin E. 37 1978 \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions. Zbl 1035.30025 Ismail, Mourad E. H.; Stanton, Dennis 36 2003 Bounds for the small real and purely imaginary zeros of Bessel and related functions. Zbl 0845.33003 Ismail, Mourad E. H.; Muldoon, Martin E. 35 1995 Asymptotics of \(q\)-orthogonal polynomials and a \(q\)-Airy function. Zbl 1072.33014 Ismail, Mourad E. H. 34 2005 Inequalities and monotonicity properties for gamma and \(q\)-gamma functions. Zbl 0819.33001 Ismail, Mourad E.; Muldoon, Martin E. 33 1994 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. 32 1988 Bessel functions and the infinite divisibility of the Student \(t\)-distribution. Zbl 0369.60023 Ismail, Mourad E. H. 30 1977 On a generalization of Szasz operators. Zbl 0385.41015 Ismail, Mourad El-Houssieny 30 1974 Analytic properties of complex Hermite polynomials. Zbl 1339.33015 Ismail, Mourad E. H. 30 2016 The associated ultraspherical polynomials and their q-analogues. Zbl 0451.33003 Bustoz, Joaquin; Ismail, Mourad E. H. 28 1982 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 28 2013 \(q\)-Hermite polynomials and classical orthogonal polynomials. Zbl 0858.33015 Berg, Christian; Ismail, Mourad E. H. 27 1996 Thermodynamic relations of the Hermitian matrix ensembles. Zbl 1042.82550 Chen, Yang; Ismail, Mourad E. H. 27 1997 A discrete approach to monotonicity of zeros of orthogonal polynomials. Zbl 0718.33004 Ismail, Mourad E. H.; Muldoon, Martin E. 26 1991 On asymptotics of Jacobi polynomials. Zbl 0735.33004 Chen, Li-Chen; Ismail, Mourad E. H. 25 1991 Small eigenvalues of large Hankel matrices: The indeterminate case. Zbl 1018.47020 Berg, Christian; Chen, Yang; Ismail, Mourad E. H. 25 2002 Monotonicity properties of determinants of special functions. Zbl 1117.33004 Ismail, Mourad E. H.; Laforgia, Andrea 24 2007 Asymptotic and generating relations for the \(q\)-Jacobi and \(_4\phi_3\) polynomials. Zbl 0489.33011 Ismail, Mourad E. H.; Wilson, James A. 24 1982 Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction. Zbl 0526.33009 Al-Salam, Waleed A.; Ismail, Mourad E. H. 24 1983 Applications of \(q\)-Taylor theorems. Zbl 1024.33012 Ismail, Mourad E. H.; Stanton, Dennis 24 2003 The Askey-Wilson operator and summation theorems. Zbl 0839.33010 Ismail, Mourad E. H. 23 1995 Classical orthogonal polynomials as moments. Zbl 0882.33012 Ismail, Mourad E. H.; Stanton, Dennis 23 1997 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 23 2014 The basic Bessel functions and polynomials. Zbl 0456.33005 Ismail, Mourad E. H. 22 1981 On the Hellmann-Feynman theorem and the variation of zeros of certain special functions. Zbl 0684.33004 Ismail, Mourad E. H.; Zhang, Ruiming 21 1988 Spectral properties of operators using tridiagonalization. Zbl 1248.33019 Ismail, Mourad E. H.; Koelink, Erik 21 2012 On sieved orthogonal polynomials. X: General blocks of recurrence relations. Zbl 0805.33006 Charris, Jairo A.; Ismail, Mourad E. H.; Monsalve, Sergio 21 1994 Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. Zbl 1351.33010 Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei 21 2016 q-beta integrals and the q-Hermite polynomials. Zbl 0658.33002 Al-Salam, W. A.; Ismail, Mourad E. H. 20 1988 More on electrostatic models for zeros of orthogonal polynomials. Zbl 0981.42015 Ismail, Mourad E. H. 20 2000 \(q\)-integral and moment representations for \(q\)-orthogonal polynomials. Zbl 1009.33015 Ismail, Mourad E. H.; Stanton, Dennis 20 2002 Zeros of entire functions and a problem of Ramanujan. Zbl 1107.33018 Ismail, Mourad E. H.; Zhang, Changgui 19 2007 Sieved orthogonal polynomials. VII: Generalized polynomial mappings. Zbl 0790.33007 Charris, Jairo A.; Ismail, Mourad E. H. 19 1993 The variation of zeros of certain orthogonal polynomials. Zbl 0628.33001 Ismail, Mourad E. H. 18 1987 On sieved orthogonal polynomials. V: Sieved Pollaczek polynomials. Zbl 0645.33018 Charris, Jairo A.; Ismail, Mourad E. H. 18 1987 Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. I. Zbl 0681.33011 Ismail, Mourad E. H.; Libis, Carl A. 18 1989 Ladder operators for \(q\)-orthogonal polynomials. Zbl 1154.33010 Chen, Yang; Ismail, Mourad E. H. 18 2008 The \(J\)-matrix method. Zbl 1216.33020 Ismail, Mourad E. H.; Koelink, Erik 18 2011 Permutation problems and special functions. Zbl 0313.05005 Askey, Richard; Ismail, Mourad E. H. 18 1976 Difference equations and quantized discriminants for \(q\)-orthogonal polynomials. Zbl 1032.33012 Ismail, Mourad E. H. 18 2003 Some indetermining moment problems and Freud-like weights. Zbl 0913.30024 Chen, Yang; Ismail, M. E. H. 17 1998 The \(q\)-Laguerre polynomials and related moment problems. Zbl 0893.33009 Ismail, Mourad E. H.; Rahman, Mizan 17 1998 Two families of associated Wilson polynomials. Zbl 0712.33005 Ismail, M. E. H.; Letessier, J.; Valent, G.; Wimp, J. 17 1990 On sieved orthogonal polynomials. IX: Orthogonality on the unit circle. Zbl 0771.33007 Ismail, Mourad E. H.; Li, Xin 17 1992 The Askey-Wilson polynomials and \(q\)-Sturm-Liouville problems. Zbl 0860.33012 Brown, B. Malcolm; Evans, W. Desmond; Ismail, Mourad E. H. 16 1996 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. 16 1996 Discriminants and functional equations for polynomials orthogonal on the unit circle. Zbl 0982.33004 Ismail, Mourad E. H.; Witte, Nicholas S. 16 2001 Three routes to the exact asymptotics for the one-dimensional quantum walk. Zbl 1049.82025 Carteret, Hilary A.; Ismail, Mourad E. H.; Richmond, Bruce 16 2003 Inequalities involving gamma and psi functions. Zbl 1042.33002 Clark, W. Edwin; Ismail, Mourad E. H. 16 2003 On the positivity of some \(_1F_2\)’s. Zbl 0301.33002 Fields, Jerry L.; Ismail, Mourad El-Houssieny 16 1975 Complex Hermite polynomials: their combinatorics and integral operators. Zbl 1308.05009 Ismail, Mourad E. H.; Simeonov, Plamen 16 2015 Quantum mechanics without potential function. Zbl 1330.81105 Alhaidari, A. D.; Ismail, M. E. H. 16 2015 Some combinatorial and analytical identities. Zbl 1256.05021 Ismail, Mourad E. H.; Stanton, Dennis 16 2012 Quadratic birth and death processes and associated continuous dual Hahn polynomials. Zbl 0692.33009 Ismail, Mourad E. H.; Letessier, Jean; Valent, Galliano 15 1989 Difference equations and discriminants for discrete orthogonal polynomials. Zbl 1081.33014 Ismail, Mourad E. H.; Nikolova, Inna; Simeonov, Plamen 15 2004 Integral representations and complete monotonicity of various quotients of Bessel functions. Zbl 0343.33005 Ismail, Mourad E. H. 15 1977 A queueing model and a set of orthogonal polynomials. Zbl 0579.60093 Ismail, Mourad E. H. 15 1985 A \(q\)-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem. Zbl 1053.33002 Ismail, Mourad E.; Zayed, Ahmed I. 15 2003 Turán type inequalities for Tricomi confluent hypergeometric functions. Zbl 1273.33006 Baricz, Árpád; Ismail, Mourad E. H. 15 2013 On sampling theory and basic Sturm-Liouville systems. Zbl 1128.39014 Annaby, M. H.; Bustoz, J.; Ismail, M. E. H. 14 2007 Discriminants and functions of the second kind of orthogonal polynomials. Zbl 0911.42012 Ismail, Mourad E. H. 14 1998 Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials. Zbl 0997.33008 Ismail, Mourad E. H.; Rahman, Mizan 14 2002 Strong asymptotics for Krawtchouk polynomials. Zbl 0948.41018 Ismail, Mourad E. H.; Simeonov, Plamen 14 1998 On sieved orthogonal polynomials. I: Symmetric Pollaczek analogues. Zbl 0576.33005 Ismail, Mourad E. H. 14 1985 On sieved orthogonal polynomials. III: Orthogonality on several intervals. Zbl 0612.33009 Ismail, Mourad E. H. 14 1986 Relation between polynomials orthogonal on the unit circle with respect to different weights. Zbl 0752.33004 Ismail, Mourad E. H.; Ruedemann, Richard W. 14 1992 Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials. Zbl 1259.05022 Ismail, Mourad E. H.; Kasraoui, Anisse; Zeng, Jiang 14 2013 On sieved orthogonal polynomials. IV. Generating functions. Zbl 0645.33017 Ismail, Mourad E. H. 13 1986 Complete monotonicity of modified Bessel functions. Zbl 0685.33004 Ismail, Mourad E. H. 13 1990 More orthogonal polynomials as moments. Zbl 0905.05083 Ismail, Mourad E. H.; Stanton, Dennis 13 1998 Lattice paths and positive trigonometric sums. Zbl 0924.42004 Ismail, M. E. H.; Kim, D.; Stanton, D. 13 1999 On differential equations for orthogonal polynomials. Zbl 0932.33007 Ismail, Mourad E. H.; Wimp, Jet 13 1998 The attractive Coulomb potential polynomials. Zbl 0584.42016 Bank, Edward; Ismail, Mourad E. H. 13 1985 \(q\)-fractional Askey-Wilson integrals and related semigroups of operators. Zbl 07631007 Ismail, Mourad E. H.; Zhang, Ruiming; Zhou, Keru 2 2022 The legacy of Dick Askey (1933–2019). Zbl 1493.01048 Cohl, Howard S.; Ismail, Mourad E. H.; Wu, Hung-Hsi 1 2022 Encyclopedia of special functions: the Askey-Bateman project. Volume 1. Univariate orthogonal polynomials. With the assistance by Walter van Assche. Zbl 1466.33001 10 2020 The asymptotic iteration method revisited. Zbl 1443.34021 Ismail, Mourad E. H.; Saad, Nasser 4 2020 Solutions of the Al-Salam-Chihara and allied moment problems. Zbl 1432.33017 Ismail, Mourad E. H. 2 2020 A discrete and \(q\) asymptotic iteration method. Zbl 1454.39010 Ismail, Mourad E. H.; Saad, Nasser 1 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. 1 2020 On a Ramanujan type entire function and its zeros. Zbl 1445.30015 Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng 1 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 11 2019 Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice. Zbl 1431.33011 Ismail, Mourad E. H.; Koelink, Erik; Román, Pablo 9 2019 Doubly infinite Jacobi matrices revisited: resolvent and spectral measure. Zbl 07003588 Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng 6 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. 4 2019 A \(q\)-translation approach to Liu’s calculus. Zbl 1433.05045 Aslan, Hatice; Ismail, Mourad E. H. 4 2019 On quasi-orthogonal polynomials: their differential equations, discriminants and electrostatics. Zbl 1479.33008 Ismail, Mourad E. H.; Wang, Xiang-Sheng 3 2019 Spectral analysis of two doubly infinite Jacobi matrices with exponential entries. Zbl 07011433 Ismail, Mourad E. H.; Štampach, František 3 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 1 2019 \(q\)-Bessel functions and Rogers-Ramanujan type identities. Zbl 1409.11082 Ismail, Mourad E. H.; Zhang, Ruiming 11 2018 Integral and series representations of \(q\)-polynomials and functions. I. Zbl 1387.33022 Ismail, Mourad E. H.; Zhang, Ruiming 7 2018 Generalized Burchnall-type identities for orthogonal polynomials and expansions. Zbl 1393.33013 Ismail, Mourad E. H.; Koelink, Erik; Román, Pablo 6 2018 On some \(2D\) orthogonal \(q\)-polynomials. Zbl 1380.33004 Ismail, Mourad E. H.; Zhang, Ruiming 10 2017 A review of multivariate orthogonal polynomials. Zbl 1371.33025 Ismail, Mourad E. H.; Zhang, Ruiming 7 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 4 2017 Diophantine properties of orthogonal polynomials and rational functions. Zbl 1362.33012 Ismail, Mourad E. H.; Rahman, Mizan 3 2017 Inequalities for gamma and \(q\)-gamma functions of complex arguments. Zbl 1371.33004 Ismail, Mourad E. H. 3 2017 Combinatorial and analytic properties of the \(n\)-dimensional Hermite polynomials. Zbl 1366.33012 Ismail, Mourad E. H.; Simeonov, Plamen 1 2017 Analytic properties of complex Hermite polynomials. Zbl 1339.33015 Ismail, Mourad E. H. 30 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 21 2016 Classes of bivariate orthogonal polynomials. Zbl 1333.33019 Ismail, Mourad E. H.; Zhang, Ruiming 11 2016 Kibble-Slepian formula and generating functions for 2D polynomials. Zbl 1347.33022 Ismail, Mourad E. H.; Zhang, Ruiming 8 2016 Formulas and identities involving the Askey-Wilson operator. Zbl 1336.33026 Ismail, Mourad E. H.; Simeonov, Plamen 4 2016 Complex Hermite polynomials: their combinatorics and integral operators. Zbl 1308.05009 Ismail, Mourad E. H.; Simeonov, Plamen 16 2015 Quantum mechanics without potential function. Zbl 1330.81105 Alhaidari, A. D.; Ismail, M. E. H. 16 2015 A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials. Zbl 1305.33026 Ismail, Mourad E. H.; Zeng, Jiang 9 2015 Two variable extensions of the Laguerre and disc polynomials. Zbl 1309.33015 Ismail, Mourad E. H.; Zeng, Jiang 8 2015 Expansions in the Askey-Wilson polynomials. Zbl 1309.33020 Ismail, Mourad E. H.; Stanton, Dennis 8 2015 On certain dual \(q\)-integral equations. Zbl 1316.45004 Ashour, Ola A.; Ismail, Mourad E. H.; Mansour, Zeinab S. 4 2015 Asymptotics for Laguerre polynomials with large order and parameters. Zbl 1315.33013 Dai, Dan; Ismail, Mourad E. H.; Wang, Jun 2 2015 Landau constants and their \(q\)-analogues. Zbl 1312.41041 Ismail, Mourad E. H.; Li, Xin; Rahman, M. 2 2015 Heine representations and monotonicity properties of determinants and Pfaffians. Zbl 1346.15005 Ismail, Mourad E. H.; Simeonov, Plamen 1 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 23 2014 Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. Zbl 1315.41014 Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng 8 2014 Functions of the second kind for classical polynomials. Zbl 1285.33013 Ismail, Mourad E. H.; Mansour, Zeinab S. I. 2 2014 On the Atkin polynomials. Zbl 1311.33009 El-Guindy, Ahmad; Ismail, Mourad E. H. 1 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 28 2013 Turán type inequalities for Tricomi confluent hypergeometric functions. Zbl 1273.33006 Baricz, Árpád; Ismail, Mourad E. H. 15 2013 Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials. Zbl 1259.05022 Ismail, Mourad E. H.; Kasraoui, Anisse; Zeng, Jiang 14 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. 9 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. 7 2013 Spectral decomposition and matrix-valued orthogonal polynomials. Zbl 1286.42035 Groenevelt, Wolter; Ismail, Mourad E. H.; Koelink, Erik 7 2013 Asymptotics of generalized derangements. Zbl 1270.33004 Ismail, Mourad E. H.; Simeonov, Plamen 3 2013 Plancherel-Rotach asymptotics for \(q\)-orthogonal polynomials. Zbl 1272.33019 Ismail, Mourad E. H.; Li, Xin 2 2013 Spectral properties of operators using tridiagonalization. Zbl 1248.33019 Ismail, Mourad E. H.; Koelink, Erik 21 2012 Some combinatorial and analytical identities. Zbl 1256.05021 Ismail, Mourad E. H.; Stanton, Dennis 16 2012 Spectral analysis of certain Schrödinger operators. Zbl 1270.30003 Ismail, Mourad E. H.; Koelink, Erik 13 2012 Some orthogonal polynomials arising from coherent states. Zbl 1245.81052 Ali, S. Twareque; Ismail, Mourad E. H. 4 2012 Connection relations and characterizations of orthogonal polynomials. Zbl 1248.33033 Ismail, Mourad E. H.; Simeonov, Plamen 3 2012 The Dirac-Coulomb problem: a mathematical revisit. Zbl 1255.81131 Alhaidari, A. D.; Bahlouli, H.; Ismail, M. E. H. 3 2012 Orthogonal basic hypergeometric Laurent polynomials. Zbl 1270.33009 Ismail, Mourad E. H.; Stanton, Dennis 1 2012 The \(J\)-matrix method. Zbl 1216.33020 Ismail, Mourad E. H.; Koelink, Erik 18 2011 Connection relations and expansions. Zbl 1235.05020 Ismail, Mourad E. H.; Rahman, Mizan 9 2011 Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials. Zbl 1215.39007 Ismail, Mourad E. H.; Simeonov, Plamen 5 2011 Equations of motion for zeros of orthogonal polynomials related to the Toda lattices. Zbl 1216.33024 Ismail, Mourad E. H.; Ma, Wen-Xiu 5 2011 On a family of positive linear integral operators. Zbl 1248.41026 Ismail, Mourad; Simeonov, Plamen 3 2011 Characterizations of continuous and discrete \(q\)-ultraspherical polynomials. Zbl 1214.33010 Ismail, Mourad E. H.; Obermaier, Josef 3 2011 Structure relations for \(q\)-polynomials and some applications. Zbl 1216.33039 Ismail, Mourad E. H.; Johnston, Sarah Jane; Mansour, Zeinab Sayed 3 2011 Orthogonal polynomials, their recursions, and functional equations. Zbl 1234.33013 Ismail, Mourad E. H. 1 2011 Hypergeometric origins of Diophantine properties associated with the Askey scheme. Zbl 1193.33016 Chen, Yang; Ismail, Mourad E. H. 8 2010 \(q\)-analogues of Freud weights and nonlinear difference equations. Zbl 1211.39007 Ismail, Mourad E. H.; Mansour, Z. S. I. 7 2010 Addition theorems via continued fractions. Zbl 1194.33017 Ismail, Mourad E. H.; Zeng, Jiang 2 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 Ismail, Mourad E. H. 115 2009 \(q\)-difference operators for orthogonal polynomials. Zbl 1185.39005 Ismail, Mourad E. H.; Simeonov, Plamen 41 2009 One parameter generalizations of the Fibonacci and Lucas numbers. Zbl 1234.11016 Ismail, Mourad E. H. 7 2009 Structure relations for orthogonal polynomials. Zbl 1166.42014 Ismail, Mourad E. H. 4 2009 Ladder operators for \(q\)-orthogonal polynomials. Zbl 1154.33010 Chen, Yang; Ismail, Mourad E. H. 18 2008 Resultants of Chebyshev polynomials. Zbl 1194.12001 Gishe, Jemal; Ismail, Mourad E. H. 9 2008 Linear \(q\)-difference equations. Zbl 1143.39009 Abu Risha, M. H.; Annaby, M. H.; Ismail, M. E. H.; Mansour, Z. S. 46 2007 Monotonicity properties of determinants of special functions. Zbl 1117.33004 Ismail, Mourad E. H.; Laforgia, Andrea 24 2007 Zeros of entire functions and a problem of Ramanujan. Zbl 1107.33018 Ismail, Mourad E. H.; Zhang, Changgui 19 2007 On sampling theory and basic Sturm-Liouville systems. Zbl 1128.39014 Annaby, M. H.; Bustoz, J.; Ismail, M. E. H. 14 2007 Scaled asymptotics for \(q\)-orthogonal polynomials. Zbl 1110.33011 Ismail, Mourad E. H.; Zhang, Ruiming 6 2007 Generalizations of Chebyshev polynomials and polynomial mappings. Zbl 1176.33011 Chen, Yang; Griffin, James; Ismail, Mourad E. H. 4 2007 Inequalities and asymptotics for a terminating \({}_4F_3\) series. Zbl 1156.33002 Ismail, Mourad E. H.; Simeonov, Plamen 2 2007 Completely monotonic functions involving the gamma and \(q\)-gamma functions. Zbl 1085.33001 Grinshpan, Arcadii Z.; Ismail, Mourad E. H. 54 2006 A moment problem and a family of integral evaluations. Zbl 1089.33016 Christiansen, Jacob S.; Ismail, Mourad E. H. 11 2006 Chaotic and periodic asymptotics for \(q\)-orthogonal polynomials. Zbl 1109.33025 Ismail, Mourad E. H.; Zhang, Ruiming 10 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. 9 2006 Functional inequalities for incomplete gamma and related functions. Zbl 1098.33001 Ismail, Mourad E. H.; Laforgia, Andrea 5 2006 Differential coefficients of orthogonal matrix polynomials. Zbl 1100.42017 Duran, Antonio J.; Ismail, Mourad E. H. 4 2006 Ramanujan continued fractions via orthogonal polynomials. Zbl 1103.11003 Ismail, Mourad E. H.; Stanton, Dennis 2 2006 On formulas of Ramanujan and Evans. Zbl 1106.33005 Ismail, Mourad E. H. 2 2006 Orthogonal polynomials and Ramanujan’s \(q\)-continued fractions. Zbl 1107.33010 Ismail, Mourad E. H.; Li, Xin 1 2006 Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Zbl 1082.42016 Ismail, Mourad E. H. 482 2005 Jacobi polynomials from compatibility conditions. Zbl 1057.33004 Chen, Yang; Ismail, Mourad 38 2005 Asymptotics of \(q\)-orthogonal polynomials and a \(q\)-Airy function. Zbl 1072.33014 Ismail, Mourad E. H. 34 2005 Determinants with orthogonal polynomial entries. Zbl 1083.15011 Ismail, Mourad E. H. 13 2005 New proofs of some \(q\) -series results. Zbl 1219.33019 Ismail, Mourad E. H.; Zhang, Ruiming 5 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 1 2005 Difference equations and discriminants for discrete orthogonal polynomials. Zbl 1081.33014 Ismail, Mourad E. H.; Nikolova, Inna; Simeonov, Plamen 15 2004 \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions. Zbl 1035.30025 Ismail, Mourad E. H.; Stanton, Dennis 36 2003 Applications of \(q\)-Taylor theorems. Zbl 1024.33012 Ismail, Mourad E. H.; Stanton, Dennis 24 2003 ...and 179 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,229 Authors 149 Ismail, Mourad El-Houssieny 56 Chen, Yang 45 Zhedanov, Alexei S. 42 Vinet, Luc 41 Baricz, Árpád 40 Srivastava, Hari Mohan 38 Marcellán Español, Francisco 35 Van Assche, Walter 28 Qi, Feng 27 Sri Ranga, Alagacone 27 Zhang, Ruiming 26 Koelink, Erik 25 Castillo, Kenier 23 Cao, Jian 22 Alhaidari, Abdulaziz D. 21 Area, Iván 21 Filipuk, Galina V. 21 Tariboon, Jessada 21 Yang, Zhenhang 20 Rahman, Mizan 20 Stanton, Dennis W. 19 Jordaan, Kerstin 18 Branquinho, Amílcar José Pinto Lopes 18 Ntouyas, Sotiris K. 18 Wong, Roderick Sue-Chuen 18 Zeng, Jiang 17 Berg, Christian 17 Dimitrov, Dimitar K. 17 Gupta, Vijay 16 Khan, Bilal 16 Khan, Nazar 16 Szabłowski, Paweł Jerzy 15 Alzer, Horst 15 Bouzeffour, Fethi 15 Dominici, Diego Ernesto 15 Godoy, Eduardo Paciência 15 Simeonov, Plamen C. 15 Zhu, Mengkun 14 Foulquié Moreno, Ana Pilar 14 Petronilho, José C. 13 Ahmad, Qazi Zahoor 13 Atakishiev, Natig M. 13 Bryc, Włodzimierz 13 Darus, Maslina 13 Karp, Dmitriĭ Borisovich 13 Martínez-Finkelshtein, Andrei 12 Annaby, Mahmoud H. 12 Ghanmi, Allal 12 Mansour, Zeinab S. I. 12 Muldoon, Martin E. 12 Tian, Jingfeng 12 Tsujimoto, Satoshi 11 Bracciali, Cleonice Fátima 11 Chu, Wenchang 11 Driver, Kathy A. 11 Forrester, Peter J. 11 Guo, Bai-Ni 11 Mouayn, Zouhaïr 11 Wang, Xiangsheng 11 Zhao, Yuqiu 10 Abreu, Luís Daniel 10 Ahmad, Bashir 10 Chung, Won-Sang 10 Genest, Vincent X. 10 Koepf, Wolfram A. 10 Mañas, Manuel 10 Štampach, František 10 Swaminathan, Anbhu 10 Tahir, Muhammad 9 Chu, Yuming 9 Dehesa, Jesús S. 9 Derevyagin, Maxim S. 9 Fitouhi, Ahmed 9 Foupouagnigni, Mama 9 Griffin, James C. 9 Koornwinder, Tom H. 9 Mbouna, D. 9 Rafaeli, Fernando Rodrigo 9 Ronveaux, André 9 Sasaki, Ryu 9 Schlosser, Michael J. 9 Suslov, Sergei K. 8 Cohl, Howard Saul 8 Dai, Dan 8 Grünbaum, Francisco Alberto 8 Guo, Victor J. W. 8 Hassanabadi, Hassan 8 Masjed-Jamei, Mohammad 8 Mehrez, Khaled 8 Min, Chao 8 Moreno-Balcázar, Juan José 8 Nevai, Paul G. 8 Pogány, Tibor K. 8 Szwarc, Ryszard 8 Valent, Galliano 8 van Diejen, Jan Felipe 8 Zhang, Lun 8 Zhang, Zhizheng 7 Agrawal, Purshottam Narain 7 Aktaş, Rabia ...and 2,129 more Authors all top 5 Cited in 396 Serials 199 Journal of Mathematical Analysis and Applications 155 Journal of Approximation Theory 130 Journal of Computational and Applied Mathematics 125 Proceedings of the American Mathematical Society 113 The Ramanujan Journal 89 Journal of Mathematical Physics 60 Integral Transforms and Special Functions 53 Advances in Applied Mathematics 46 Applied Mathematics and Computation 43 Constructive Approximation 41 Journal of Difference Equations and Applications 38 Advances in Difference Equations 37 Transactions of the American Mathematical Society 31 Advances in Mathematics 25 Journal of Combinatorial Theory. Series A 24 SIGMA. 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A 6 The Annals of Probability 6 Numerical Functional Analysis and Optimization 6 Journal of Symbolic Computation 6 Applied Mathematics Letters 6 Aequationes Mathematicae 6 Bulletin des Sciences Mathématiques 6 Advances in Computational Mathematics 6 Arab Journal of Mathematical Sciences 6 Annals of Combinatorics 6 Journal of Nonlinear Mathematical Physics 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Statistical Mechanics: Theory and Experiment 5 Bulletin of the Australian Mathematical Society 5 Journal d’Analyse Mathématique 5 Nuclear Physics. 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Mathematics 4 Modern Physics Letters A 4 Mathematical Notes 4 Physica A 4 Demonstratio Mathematica 4 Integral Equations and Operator Theory 4 Journal of Differential Equations ...and 296 more Serials all top 5 Cited in 58 Fields 1,553 Special functions (33-XX) 500 Harmonic analysis on Euclidean spaces (42-XX) 344 Combinatorics (05-XX) 306 Functions of a complex variable (30-XX) 250 Number theory (11-XX) 241 Difference and functional equations (39-XX) 241 Approximations and expansions (41-XX) 240 Real functions (26-XX) 230 Probability theory and stochastic processes (60-XX) 190 Ordinary differential equations (34-XX) 178 Quantum theory (81-XX) 151 Operator theory (47-XX) 150 Linear and multilinear algebra; matrix theory (15-XX) 100 Integral transforms, operational calculus (44-XX) 98 Numerical analysis (65-XX) 82 Partial differential equations (35-XX) 57 Statistical mechanics, structure of matter (82-XX) 54 Functional analysis (46-XX) 53 Dynamical systems and ergodic theory (37-XX) 49 Nonassociative rings and algebras (17-XX) 47 Statistics (62-XX) 39 Information and communication theory, circuits (94-XX) 34 Sequences, series, summability (40-XX) 20 Field theory and polynomials (12-XX) 19 Integral equations (45-XX) 19 Operations research, mathematical programming (90-XX) 18 Optics, electromagnetic theory (78-XX) 17 Topological groups, Lie groups (22-XX) 17 Computer science (68-XX) 17 Biology and other natural sciences (92-XX) 16 Several complex variables and analytic spaces (32-XX) 14 Abstract harmonic analysis (43-XX) 14 Relativity and gravitational theory (83-XX) 13 History and biography (01-XX) 13 Algebraic geometry (14-XX) 12 Group theory and generalizations (20-XX) 12 Potential theory (31-XX) 10 Commutative algebra (13-XX) 9 Mechanics of particles and systems (70-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 General and overarching topics; collections (00-XX) 7 Fluid mechanics (76-XX) 6 Associative rings and algebras (16-XX) 6 Measure and integration (28-XX) 6 Convex and discrete geometry (52-XX) 6 Differential geometry (53-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Geometry (51-XX) 4 Systems theory; control (93-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Manifolds and cell complexes (57-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 1 Category theory; homological algebra (18-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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