Ismail, Mourad E. H.; Zhou, Keru \(q\)-fractional integral operators with two parameters. (English) Zbl 07789126 Adv. Appl. Math. 154, Article ID 102638, 16 p. (2024). MSC: 33D45 47D03 33C45 45P05 26A33 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{K. Zhou}, Adv. Appl. Math. 154, Article ID 102638, 16 p. (2024; Zbl 07789126) Full Text: DOI arXiv
Bhatnagar, Gaurav; Ismail, Mourad E. H. Orthogonal polynomials associated with a continued fraction of Hirschhorn. (English) Zbl 07695116 Ramanujan J. 61, No. 2, 487-514 (2023). MSC: 33D45 30B70 11A55 PDFBibTeX XMLCite \textit{G. Bhatnagar} and \textit{M. E. H. Ismail}, Ramanujan J. 61, No. 2, 487--514 (2023; Zbl 07695116) Full Text: DOI arXiv
Dimitrov, Dimitar K.; Gadjev, Ivan; Ismail, Mourad E. H. Sharp Hardy’s Inequalities in Hilbert Spaces. arXiv:2306.08172 Preprint, arXiv:2306.08172 [math.CA] (2023). MSC: 26D10 26D15 33D45 BibTeX Cite \textit{D. K. Dimitrov} et al., ``Sharp Hardy's Inequalities in Hilbert Spaces'', Preprint, arXiv:2306.08172 [math.CA] (2023) Full Text: arXiv OA License
Ismail, Mourad E. H.; Zhang, Ruiming; Zhou, Keru \(q\)-fractional Askey-Wilson integrals and related semigroups of operators. (English) Zbl 07631007 Physica D 442, Article ID 133534, 15 p. (2022). MSC: 47D03 26A33 33D45 41A35 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., Physica D 442, Article ID 133534, 15 p. (2022; Zbl 07631007) Full Text: DOI arXiv
Ismail, Mourad E. H.; Zhang, Ruiming Integral and series representations of \(q\)-polynomials and functions. III: Theta, Ramanujan and \(q\)-Bessel functions. (English) Zbl 1506.33010 Anal. Appl., Singap. 20, No. 1, 1-18 (2022). MSC: 33D15 33D05 33D45 33D60 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Anal. Appl., Singap. 20, No. 1, 1--18 (2022; Zbl 1506.33010) Full Text: DOI
Ismail, Mourad E. H.; Zhang, Ruiming Completely monotonic Fredholm determinants. (English) Zbl 1481.33010 Baumann, Gerd (ed.), New sinc methods of numerical analysis. Festschrift in honor of Frank Stenger’s 80th birthday. Based on the presentations at the symposium, Rhodes, Greece, September 13–18, 2018. Cham: Birkhäuser. Trends Math., 299-321 (2021). MSC: 33C47 15B52 26A48 45B05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, in: New sinc methods of numerical analysis. Festschrift in honor of Frank Stenger's 80th birthday. Based on the presentations at the symposium, Rhodes, Greece, September 13--18, 2018. Cham: Birkhäuser. 299--321 (2021; Zbl 1481.33010) Full Text: DOI
Bhatnagar, Gaurav; Ismail, Mourad El-Houssieny On entry II.16.12: a continued fraction of Ramanujan. (English) Zbl 1476.11014 Int. J. Number Theory 17, No. 2, 251-266 (2021). Reviewer: Michael M. Pahirya (Mukachevo) MSC: 11A55 33D45 30B70 PDFBibTeX XMLCite \textit{G. Bhatnagar} and \textit{M. E. H. Ismail}, Int. J. Number Theory 17, No. 2, 251--266 (2021; Zbl 1476.11014) Full Text: DOI arXiv
Cohl, Howard S. (ed.); Ismail, Mourad E. H. (ed.) Lectures on orthogonal polynomials and special functions. Based on the 6th summer school on orthogonal polynomials and special functions (OPSF-S6), University of Maryland, College Park, MD, USA, July 11–15, 2016. (English) Zbl 1460.33001 London Mathematical Society Lecture Note Series 464. Cambridge: Cambridge University Press (ISBN 978-1-108-82159-9/pbk; 978-1-108-90899-3/ebook). xvi, 334 p. (2021). MSC: 33-06 42-06 33C67 42C05 00B25 PDFBibTeX XMLCite \textit{H. S. Cohl} (ed.) and \textit{M. E. H. Ismail} (ed.), Lectures on orthogonal polynomials and special functions. Based on the 6th summer school on orthogonal polynomials and special functions (OPSF-S6), University of Maryland, College Park, MD, USA, July 11--15, 2016. Cambridge: Cambridge University Press (2021; Zbl 1460.33001) Full Text: DOI
Ismail, Mourad E. H.; Simeonov, Plamen Multivariate holomorphic Hermite polynomials. (English) Zbl 1475.33003 Ramanujan J. 53, No. 2, 357-387 (2020). Reviewer: María-José Cantero (Zaragoza) MSC: 33C45 33C50 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Ramanujan J. 53, No. 2, 357--387 (2020; Zbl 1475.33003) Full Text: DOI
Ismail, Mourad; Law, Chun-Kong A difference equation approach to Plancherel-Rotach asymptotics for \(q\)-orthogonal polynomials. (English) Zbl 1473.39008 Stud. Appl. Math. 145, No. 4, 696-718 (2020). Reviewer: Hakan Adıgüzel (Serdivan) MSC: 39A13 33E30 33D05 33D45 05A30 PDFBibTeX XMLCite \textit{M. Ismail} and \textit{C.-K. Law}, Stud. Appl. Math. 145, No. 4, 696--718 (2020; Zbl 1473.39008) Full Text: DOI
Ismail, Mourad E. H.; Simeonov, Plamen Connection relations for \(q\)-Taylor polynomial bases. (English) Zbl 1435.33018 Adv. Appl. Math. 117, Article ID 102015, 20 p. (2020). MSC: 33D15 33D45 41A58 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Adv. Appl. Math. 117, Article ID 102015, 20 p. (2020; Zbl 1435.33018) Full Text: DOI
Ismail, Mourad E. H. Solutions of the Al-Salam-Chihara and allied moment problems. (English) Zbl 1432.33017 Anal. Appl., Singap. 18, No. 2, 185-210 (2020). MSC: 33D45 30E05 33C45 42A65 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Anal. Appl., Singap. 18, No. 2, 185--210 (2020; Zbl 1432.33017) Full Text: DOI
Aslan, Hatice; Ismail, Mourad E. H. A \(q\)-translation approach to Liu’s calculus. (English) Zbl 1433.05045 Ann. Comb. 23, No. 3-4, 465-488 (2019). MSC: 05A30 05A40 33D45 PDFBibTeX XMLCite \textit{H. Aslan} and \textit{M. E. H. Ismail}, Ann. Comb. 23, No. 3--4, 465--488 (2019; Zbl 1433.05045) Full Text: DOI
Ismail, Mourad E. H.; Koelink, Erik; Román, Pablo Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice. (English) Zbl 1431.33011 Adv. Appl. Math. 110, 235-269 (2019). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 37K10 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., Adv. Appl. Math. 110, 235--269 (2019; Zbl 1431.33011) Full Text: DOI arXiv
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng Asymptotics of partition functions in a fermionic matrix model and of related \(q\)-polynomials. (English) Zbl 1419.81028 Stud. Appl. Math. 142, No. 1, 91-105 (2019). MSC: 81T10 33D90 41A60 14K25 60B20 33C45 PDFBibTeX XMLCite \textit{D. Dai} et al., Stud. Appl. Math. 142, No. 1, 91--105 (2019; Zbl 1419.81028) Full Text: DOI arXiv
Ismail, Mourad E. H.; Wang, Xiang-Sheng On quasi-orthogonal polynomials: their differential equations, discriminants and electrostatics. (English) Zbl 1479.33008 J. Math. Anal. Appl. 474, No. 2, 1178-1197 (2019). Reviewer: Howard Cohl (Gaithersburg) MSC: 33C47 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{X.-S. Wang}, J. Math. Anal. Appl. 474, No. 2, 1178--1197 (2019; Zbl 1479.33008) Full Text: DOI
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng Doubly infinite Jacobi matrices revisited: resolvent and spectral measure. (English) Zbl 07003588 Adv. Math. 343, 157-192 (2019). MSC: 47B36 33C45 PDFBibTeX XMLCite \textit{D. Dai} et al., Adv. Math. 343, 157--192 (2019; Zbl 07003588) Full Text: DOI
Ismail, M. E. H.; Ranga, A. Sri \(R_{II}\) type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle. (English) Zbl 1405.33017 Linear Algebra Appl. 562, 63-90 (2019). MSC: 33C47 33C45 58C40 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{A. S. Ranga}, Linear Algebra Appl. 562, 63--90 (2019; Zbl 1405.33017) Full Text: DOI arXiv
Ismail, Mourad E. H.; Koelink, Erik; Román, Pablo Generalized Burchnall-type identities for orthogonal polynomials and expansions. (English) Zbl 1393.33013 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 072, 24 p. (2018). MSC: 33C45 33D45 42C05 37K10 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 072, 24 p. (2018; Zbl 1393.33013) Full Text: DOI arXiv
Ismail, Mourad E. H.; Zhang, Ruiming \(q\)-Bessel functions and Rogers-Ramanujan type identities. (English) Zbl 1409.11082 Proc. Am. Math. Soc. 146, No. 9, 3633-3646 (2018). Reviewer: Mihály Szalay (Budapest) MSC: 11P84 33D45 05A17 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Proc. Am. Math. Soc. 146, No. 9, 3633--3646 (2018; Zbl 1409.11082) Full Text: DOI arXiv
Ismail, Mourad E. H.; Zhang, Ruiming Integral and series representations of \(q\)-polynomials and functions. I. (English) Zbl 1387.33022 Anal. Appl., Singap. 16, No. 2, 209-281 (2018). MSC: 33D15 33D45 33D60 44A20 42A38 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Anal. Appl., Singap. 16, No. 2, 209--281 (2018; Zbl 1387.33022) Full Text: DOI arXiv
Ismail, Mourad E. H.; Zhang, Ruiming A review of multivariate orthogonal polynomials. (English) Zbl 1371.33025 J. Egypt. Math. Soc. 25, No. 2, 91-110 (2017). MSC: 33C50 33D50 33C45 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, J. Egypt. Math. Soc. 25, No. 2, 91--110 (2017; Zbl 1371.33025) Full Text: DOI
Ismail, Mourad E. H.; Zhang, Ruiming On some \(2D\) orthogonal \(q\)-polynomials. (English) Zbl 1380.33004 Trans. Am. Math. Soc. 369, No. 10, 6779-6821 (2017). Reviewer: James Wan (Singapore) MSC: 33C45 33C50 33D50 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Trans. Am. Math. Soc. 369, No. 10, 6779--6821 (2017; Zbl 1380.33004) Full Text: DOI arXiv
Ismail, Mourad E. H.; Zhang, Ruiming Integral and series representations of \(q\)-polynomials and functions. II: Schur polynomials and the Rogers-Ramanujan identities. (English) Zbl 1380.33010 Proc. Am. Math. Soc. 145, No. 9, 3717-3733 (2017). Reviewer: William J. Keith (Houghton) MSC: 33D45 11P84 05A17 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Proc. Am. Math. Soc. 145, No. 9, 3717--3733 (2017; Zbl 1380.33010) Full Text: DOI arXiv
Ismail, Mourad E. H.; Rahman, Mizan Diophantine properties of orthogonal polynomials and rational functions. (English) Zbl 1362.33012 Proc. Am. Math. Soc. 145, No. 6, 2427-2440 (2017). Reviewer: Peter Massopust (München) MSC: 33C45 33C20 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{M. Rahman}, Proc. Am. Math. Soc. 145, No. 6, 2427--2440 (2017; Zbl 1362.33012) Full Text: DOI
Ismail, Mourad E. H.; Simeonov, Plamen Combinatorial and analytic properties of the \(n\)-dimensional Hermite polynomials. (English) Zbl 1366.33012 J. Math. Anal. Appl. 449, No. 1, 368-381 (2017). MSC: 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, J. Math. Anal. Appl. 449, No. 1, 368--381 (2017; Zbl 1366.33012) Full Text: DOI
Ashour, O. A.; Ismail, M. E. H.; Mansour, Z. S. I. Dual and triple equations and \(q\)-orthogonal polynomials. (English) Zbl 1469.33011 J. Difference Equ. Appl. 22, No. 7, 973-988 (2016). MSC: 33D45 PDFBibTeX XMLCite \textit{O. A. Ashour} et al., J. Difference Equ. Appl. 22, No. 7, 973--988 (2016; Zbl 1469.33011) Full Text: DOI
Ismail, Mourad E. H.; Zhang, Ruiming Kibble-Slepian formula and generating functions for 2D polynomials. (English) Zbl 1347.33022 Adv. Appl. Math. 80, 70-92 (2016). MSC: 33C45 42C20 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Adv. Appl. Math. 80, 70--92 (2016; Zbl 1347.33022) Full Text: DOI arXiv
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei Tridiagonalization of the hypergeometric operator and the Racah-Wilson algebra. (English) Zbl 1351.33010 Proc. Am. Math. Soc. 144, No. 10, 4441-4454 (2016). Reviewer: Teresa A. Mesquita (Vila Nova de Famalicão) MSC: 33C45 33C80 42C05 PDFBibTeX XMLCite \textit{V. X. Genest} et al., Proc. Am. Math. Soc. 144, No. 10, 4441--4454 (2016; Zbl 1351.33010) Full Text: DOI arXiv
Ismail, Mourad E. H.; Simeonov, Plamen Formulas and identities involving the Askey-Wilson operator. (English) Zbl 1336.33026 Adv. Appl. Math. 76, 68-96 (2016). MSC: 33C45 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Adv. Appl. Math. 76, 68--96 (2016; Zbl 1336.33026) Full Text: DOI
Ismail, Mourad E. H. Analytic properties of complex Hermite polynomials. (English) Zbl 1339.33015 Trans. Am. Math. Soc. 368, No. 2, 1189-1210 (2016). Reviewer: Bujar Fejzullahu (Presevo) MSC: 33C50 33C70 42C10 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Trans. Am. Math. Soc. 368, No. 2, 1189--1210 (2016; Zbl 1339.33015) Full Text: DOI
Ismail, Mourad E. H.; Zhang, Ruiming Classes of bivariate orthogonal polynomials. (English) Zbl 1333.33019 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 021, 37 p. (2016). MSC: 33C50 33D50 33C45 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 021, 37 p. (2016; Zbl 1333.33019) Full Text: DOI arXiv
Alhaidari, A. D.; Ismail, M. E. H. Quantum mechanics without potential function. (English) Zbl 1330.81105 J. Math. Phys. 56, No. 7, 072107, 19 p. (2015). Reviewer: Michael Perelmuter (Kyïv) MSC: 81Q65 81U05 81Q05 33C47 PDFBibTeX XMLCite \textit{A. D. Alhaidari} and \textit{M. E. H. Ismail}, J. Math. Phys. 56, No. 7, 072107, 19 p. (2015; Zbl 1330.81105) Full Text: DOI arXiv
Dai, Dan; Ismail, Mourad E. H.; Wang, Jun Asymptotics for Laguerre polynomials with large order and parameters. (English) Zbl 1315.33013 J. Approx. Theory 193, 4-19 (2015). Reviewer: M. Abdessadek Saib (Lyon) MSC: 33C45 35Q15 PDFBibTeX XMLCite \textit{D. Dai} et al., J. Approx. Theory 193, 4--19 (2015; Zbl 1315.33013) Full Text: DOI
Ismail, Mourad E. H.; Simeonov, Plamen Complex Hermite polynomials: their combinatorics and integral operators. (English) Zbl 1308.05009 Proc. Am. Math. Soc. 143, No. 4, 1397-1410 (2015). MSC: 05A15 05A18 33C45 45P05 42A65 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Proc. Am. Math. Soc. 143, No. 4, 1397--1410 (2015; Zbl 1308.05009) Full Text: DOI
Ismail, Mourad E. H.; Zeng, Jiang A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials. (English) Zbl 1305.33026 Adv. Appl. Math. 64, 70-88 (2015). MSC: 33C50 33C70 05A15 05A16 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{J. Zeng}, Adv. Appl. Math. 64, 70--88 (2015; Zbl 1305.33026) Full Text: DOI
Ismail, Mourad E. H.; Stanton, Dennis Expansions in the Askey-Wilson polynomials. (English) Zbl 1309.33020 J. Math. Anal. Appl. 424, No. 1, 664-674 (2015). MSC: 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{D. Stanton}, J. Math. Anal. Appl. 424, No. 1, 664--674 (2015; Zbl 1309.33020) Full Text: DOI
Ismail, Mourad E. H.; Zeng, Jiang Two variable extensions of the Laguerre and disc polynomials. (English) Zbl 1309.33015 J. Math. Anal. Appl. 424, No. 1, 289-303 (2015). MSC: 33C50 26C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{J. Zeng}, J. Math. Anal. Appl. 424, No. 1, 289--303 (2015; Zbl 1309.33015) Full Text: DOI
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. (English) Zbl 1315.41014 Constr. Approx. 40, No. 1, 61-104 (2014). Reviewer: José L. Lopez (Pamplona) MSC: 41A60 33C47 30E05 PDFBibTeX XMLCite \textit{D. Dai} et al., Constr. Approx. 40, No. 1, 61--104 (2014; Zbl 1315.41014) Full Text: DOI arXiv
El-Guindy, Ahmad; Ismail, Mourad E. H. On the Atkin polynomials. (English) Zbl 1311.33009 Pac. J. Math. 272, No. 1, 111-130 (2014). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C47 11F03 33C05 PDFBibTeX XMLCite \textit{A. El-Guindy} and \textit{M. E. H. Ismail}, Pac. J. Math. 272, No. 1, 111--130 (2014; Zbl 1311.33009) Full Text: DOI arXiv
Ismail, Mourad E. H.; Mansour, Zeinab S. I. Functions of the second kind for classical polynomials. (English) Zbl 1285.33013 Adv. Appl. Math. 54, 66-104 (2014). MSC: 33D45 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{Z. S. I. Mansour}, Adv. Appl. Math. 54, 66--104 (2014; Zbl 1285.33013) Full Text: DOI
Dimitrov, Dimitar K.; Ismail, Mourad E. H.; Rafaeli, Fernando R. Interlacing of zeros of orthogonal polynomials under modification of the measure. (English) Zbl 1337.30003 J. Approx. Theory 175, 64-76 (2013). Reviewer: Fahreddin Abdullayev (Mersin) MSC: 30C10 30C15 33C45 PDFBibTeX XMLCite \textit{D. K. Dimitrov} et al., J. Approx. Theory 175, 64--76 (2013; Zbl 1337.30003) Full Text: DOI
Groenevelt, Wolter; Ismail, Mourad E. H.; Koelink, Erik Spectral decomposition and matrix-valued orthogonal polynomials. (English) Zbl 1286.42035 Adv. Math. 244, 91-105 (2013). MSC: 42C05 PDFBibTeX XMLCite \textit{W. Groenevelt} et al., Adv. Math. 244, 91--105 (2013; Zbl 1286.42035) Full Text: DOI arXiv
Ismail, Mourad E. H.; Simeonov, Plamen Asymptotics of generalized derangements. (English) Zbl 1270.33004 Adv. Comput. Math. 39, No. 1, 101-127 (2013). MSC: 33C45 34M30 05A15 06A07 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Adv. Comput. Math. 39, No. 1, 101--127 (2013; Zbl 1270.33004) Full Text: DOI
Ismail, Mourad E. H.; Li, Xin Plancherel-Rotach asymptotics for \(q\)-orthogonal polynomials. (English) Zbl 1272.33019 Constr. Approx. 37, No. 3, 341-356 (2013). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33D45 41A60 65Q30 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{X. Li}, Constr. Approx. 37, No. 3, 341--356 (2013; Zbl 1272.33019) Full Text: DOI arXiv
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei The Dunkl oscillator in the plane. Part I: Superintegrability, separated wavefunctions and overlap coefficients. (English) Zbl 1267.81139 J. Phys. A, Math. Theor. 46, No. 14, Article ID 145201, 21 p. (2013). MSC: 81Q05 81R12 22E70 33C45 PDFBibTeX XMLCite \textit{V. X. Genest} et al., J. Phys. A, Math. Theor. 46, No. 14, Article ID 145201, 21 p. (2013; Zbl 1267.81139) Full Text: DOI arXiv
Ismail, Mourad E. H.; Kasraoui, Anisse; Zeng, Jiang Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials. (English) Zbl 1259.05022 J. Comb. Theory, Ser. A 120, No. 3, 561-599 (2013). MSC: 05A99 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., J. Comb. Theory, Ser. A 120, No. 3, 561--599 (2013; Zbl 1259.05022) Full Text: DOI arXiv
Dimitrov, D. K.; Ismail, M. E. H.; Sri Ranga, A. A class of hypergeometric polynomials with zeros on the unit circle: extremal and orthogonal properties and quadrature formulas. (English) Zbl 1268.33007 Appl. Numer. Math. 65, 41-52 (2013). Reviewer: Luan Ozelim (Brasilia) MSC: 33C45 33C05 65D32 PDFBibTeX XMLCite \textit{D. K. Dimitrov} et al., Appl. Numer. Math. 65, 41--52 (2013; Zbl 1268.33007) Full Text: DOI
Ismail, Mourad E. H.; Stanton, Dennis Orthogonal basic hypergeometric Laurent polynomials. (English) Zbl 1270.33009 SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 092, 20 p. (2012). MSC: 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{D. Stanton}, SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 092, 20 p. (2012; Zbl 1270.33009) Full Text: DOI arXiv
Ismail, Mourad E. H.; Koelink, Erik Spectral analysis of certain Schrödinger operators. (English) Zbl 1270.30003 SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 061, 19 p. (2012). MSC: 30E05 33C45 39A10 42C05 44A60 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{E. Koelink}, SIGMA, Symmetry Integrability Geom. Methods Appl. 8, Paper 061, 19 p. (2012; Zbl 1270.30003) Full Text: DOI arXiv
Ismail, Mourad E. H.; Koelink, Erik Spectral properties of operators using tridiagonalization. (English) Zbl 1248.33019 Anal. Appl., Singap. 10, No. 3, 327-343 (2012). MSC: 33C45 39A70 42C05 34L40 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{E. Koelink}, Anal. Appl., Singap. 10, No. 3, 327--343 (2012; Zbl 1248.33019) Full Text: DOI arXiv
Ismail, Mourad E. H.; Simeonov, Plamen Connection relations and characterizations of orthogonal polynomials. (English) Zbl 1248.33033 Adv. Appl. Math. 49, No. 2, 134-164 (2012). MSC: 33D45 33C45 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Adv. Appl. Math. 49, No. 2, 134--164 (2012; Zbl 1248.33033) Full Text: DOI
Ali, S. Twareque; Ismail, Mourad E. H. Some orthogonal polynomials arising from coherent states. (English) Zbl 1245.81052 J. Phys. A, Math. Theor. 45, No. 12, Article ID 125203, 16 p. (2012). MSC: 81R30 46N50 81V80 33C47 PDFBibTeX XMLCite \textit{S. T. Ali} and \textit{M. E. H. Ismail}, J. Phys. A, Math. Theor. 45, No. 12, Article ID 125203, 16 p. (2012; Zbl 1245.81052) Full Text: DOI arXiv
Ismail, Mourad E. H. Orthogonal polynomials, their recursions, and functional equations. (English) Zbl 1234.33013 Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-13658-7/pbk). London Mathematical Society Lecture Note Series 381, 115-138 (2011). MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Lond. Math. Soc. Lect. Note Ser. 381, 115--138 (2011; Zbl 1234.33013)
Ismail, Mourad E. H.; Koelink, Erik The \(J\)-matrix method. (English) Zbl 1216.33020 Adv. Appl. Math. 46, No. 1-4, 379-395 (2011). MSC: 33C45 42C05 34L40 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{E. Koelink}, Adv. Appl. Math. 46, No. 1--4, 379--395 (2011; Zbl 1216.33020) Full Text: DOI arXiv
Ismail, Mourad E. H.; Johnston, Sarah Jane; Mansour, Zeinab Sayed Structure relations for \(q\)-polynomials and some applications. (English) Zbl 1216.33039 Appl. Anal. 90, No. 3-4, 747-767 (2011). MSC: 33D45 39A13 30E05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., Appl. Anal. 90, No. 3--4, 747--767 (2011; Zbl 1216.33039) Full Text: DOI
Ismail, Mourad E. H.; Ma, Wen-Xiu Equations of motion for zeros of orthogonal polynomials related to the Toda lattices. (English) Zbl 1216.33024 Arab J. Math. Sci. 17, No. 1, 1-10 (2011). MSC: 33C52 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{W.-X. Ma}, Arab J. Math. Sci. 17, No. 1, 1--10 (2011; Zbl 1216.33024) Full Text: DOI
Ismail, Mourad E. H.; Obermaier, Josef Characterizations of continuous and discrete \(q\)-ultraspherical polynomials. (English) Zbl 1214.33010 Can. J. Math. 63, No. 1, 181-199 (2011). Reviewer: Nele De Schepper (Gent) MSC: 33D45 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{J. Obermaier}, Can. J. Math. 63, No. 1, 181--199 (2011; Zbl 1214.33010) Full Text: DOI
Ismail, Mourad E. H.; Simeonov, Plamen Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials. (English) Zbl 1215.39007 J. Math. Anal. Appl. 376, No. 1, 259-274 (2011). Reviewer: Sui Sun Cheng (Hsinchu) MSC: 39A12 42C05 33C47 65Q30 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, J. Math. Anal. Appl. 376, No. 1, 259--274 (2011; Zbl 1215.39007) Full Text: DOI
Ismail, Mourad E. H.; Mansour, Z. S. I. \(q\)-analogues of Freud weights and nonlinear difference equations. (English) Zbl 1211.39007 Adv. Appl. Math. 45, No. 4, 518-547 (2010). Reviewer: Andrei A. Kapaev (Trieste) MSC: 39A13 42C05 33D50 33C47 33E17 41A17 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{Z. S. I. Mansour}, Adv. Appl. Math. 45, No. 4, 518--547 (2010; Zbl 1211.39007) Full Text: DOI
Ismail, Mourad E. H. Two discrete systems of \(q\)-orthogonal polynomials. (English) Zbl 1197.33017 Acosta-Humánez, Primitivo B. (ed.) et al., Differential algebra, complex analysis and orthogonal polynomials. Jairo Charris Seminar 2007–2008, Escuela de Matemáticas, Universidad Sergio Arboleda, Bogotá, Colombia. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4886-9/pbk). Contemporary Mathematics 509, 95-101 (2010). MSC: 33D45 41A60 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Contemp. Math. 509, 95--101 (2010; Zbl 1197.33017)
Chen, Yang; Ismail, Mourad E. H. Hypergeometric origins of Diophantine properties associated with the Askey scheme. (English) Zbl 1193.33016 Proc. Am. Math. Soc. 138, No. 3, 943-951 (2010). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 33C20 33C45 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{M. E. H. Ismail}, Proc. Am. Math. Soc. 138, No. 3, 943--951 (2010; Zbl 1193.33016) Full Text: DOI arXiv
Chiang, Yik-Man; Ismail, Mourad E. H. Erratum to: On value distribution theory of second order periodic ODEs, special functions and orthogonal polynomials. (English) Zbl 1185.34133 Can. J. Math. 62, No. 2, 261 (2010). Reviewer: Klaus R. Schneider (Berlin) MSC: 34M10 33C15 33C47 PDFBibTeX XMLCite \textit{Y.-M. Chiang} and \textit{M. E. H. Ismail}, Can. J. Math. 62, No. 2, 261 (2010; Zbl 1185.34133) Full Text: DOI
Ismail, Mourad E. H.; Zeng, Jiang Addition theorems via continued fractions. (English) Zbl 1194.33017 Trans. Am. Math. Soc. 362, No. 2, 957-983 (2010). Reviewer: Jeremy Lovejoy (Paris) MSC: 33D15 33C15 30E05 05A15 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{J. Zeng}, Trans. Am. Math. Soc. 362, No. 2, 957--983 (2010; Zbl 1194.33017) Full Text: DOI arXiv
Ismail, Mourad E. H.; Simeonov, Plamen \(q\)-difference operators for orthogonal polynomials. (English) Zbl 1185.39005 J. Comput. Appl. Math. 233, No. 3, 749-761 (2009). Reviewer: Jacques Sauloy (Toulouse) MSC: 39A13 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, J. Comput. Appl. Math. 233, No. 3, 749--761 (2009; Zbl 1185.39005) Full Text: DOI
Ismail, Mourad E. H. [Van Assche, Walter] Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. (English) Zbl 1172.42008 Encyclopedia of Mathematics and its Applications 98. Cambridge: Cambridge University Press (ISBN 978-0-521-14347-9/pbk). xviii, 708 p. (2009). MSC: 42C05 42C15 33D80 33C45 33C50 33D45 42-02 33-02 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Cambridge: Cambridge University Press (2009; Zbl 1172.42008)
Ismail, Mourad E. H. One parameter generalizations of the Fibonacci and Lucas numbers. (English) Zbl 1234.11016 Fibonacci Q. 46-47(2008/2009), No. 2, 167-180 (2009). MSC: 11B39 11D25 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Fibonacci Q. 46--47, No. 2, 167--180 (2009; Zbl 1234.11016) Full Text: arXiv
Ismail, Mourad E. H. Structure relations for orthogonal polynomials. (English) Zbl 1166.42014 Pac. J. Math. 240, No. 2, 309-319 (2009). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 42C05 33C45 33C47 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Pac. J. Math. 240, No. 2, 309--319 (2009; Zbl 1166.42014) Full Text: DOI
Ismail, Mourad E.; Li, Xin Functions whose moments form a geometric progression. (English) Zbl 1194.42031 De Carli, Laura (ed.) et al., Topics in classical analysis and applications in honor of Daniel Waterman. Selected papers of the 2007 South Florida Analysis Seminar, Fort Lauderdale, FL, USA, March 30–April 1, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-283-443-0/hbk). 110-117 (2008). MSC: 42C05 PDFBibTeX XMLCite \textit{M. E. Ismail} and \textit{X. Li}, in: Topics in classical analysis and applications in honor of Daniel Waterman. Selected papers of the 2007 South Florida Analysis Seminar, Fort Lauderdale, FL, USA, March 30--April 1, 2007. Hackensack, NJ: World Scientific. 110--117 (2008; Zbl 1194.42031)
Gishe, Jemal; Ismail, Mourad E. H. Resultants of Chebyshev polynomials. (English) Zbl 1194.12001 Z. Anal. Anwend. 27, No. 4, 499-508 (2008). Reviewer: Tom M. Apostol (Pasadena) MSC: 12E05 33C45 13P05 PDFBibTeX XMLCite \textit{J. Gishe} and \textit{M. E. H. Ismail}, Z. Anal. Anwend. 27, No. 4, 499--508 (2008; Zbl 1194.12001) Full Text: DOI Link
Chen, Yang; Ismail, Mourad E. H. Ladder operators for \(q\)-orthogonal polynomials. (English) Zbl 1154.33010 J. Math. Anal. Appl. 345, No. 1, 1-10 (2008). Reviewer: Semyon Yakubovich (Porto) MSC: 33D52 44A60 33C45 39A10 39A13 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{M. E. H. Ismail}, J. Math. Anal. Appl. 345, No. 1, 1--10 (2008; Zbl 1154.33010) Full Text: DOI arXiv
Ismail, Mourad E. H.; Simeonov, Plamen Inequalities and asymptotics for a terminating \({}_4F_3\) series. (English) Zbl 1156.33002 Ill. J. Math. 51, No. 3, 861-881 (2007). Reviewer: Wadim Zudilin (Bonn) MSC: 33C20 26D15 30E15 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{P. Simeonov}, Ill. J. Math. 51, No. 3, 861--881 (2007; Zbl 1156.33002) Full Text: Link
Chen, Yang; Griffin, James; Ismail, Mourad E. H. Generalizations of Chebyshev polynomials and polynomial mappings. (English) Zbl 1176.33011 Trans. Am. Math. Soc. 359, No. 10, 4787-4828 (2007). MSC: 33C45 PDFBibTeX XMLCite \textit{Y. Chen} et al., Trans. Am. Math. Soc. 359, No. 10, 4787--4828 (2007; Zbl 1176.33011) Full Text: DOI arXiv
Ismail, Mourad E. H.; Zhang, Ruiming Scaled asymptotics for \(q\)-orthogonal polynomials. (English) Zbl 1110.33011 C. R., Math., Acad. Sci. Paris 344, No. 2, 71-75 (2007). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33D45 34E05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, C. R., Math., Acad. Sci. Paris 344, No. 2, 71--75 (2007; Zbl 1110.33011) Full Text: DOI
Ismail, Mourad E. H.; Zhang, Changgui Zeros of entire functions and a problem of Ramanujan. (English) Zbl 1107.33018 Adv. Math. 209, No. 1, 363-380 (2007). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33D45 33E05 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{C. Zhang}, Adv. Math. 209, No. 1, 363--380 (2007; Zbl 1107.33018) Full Text: DOI
Ismail, Mourad E. H.; Zhang, Ruiming Chaotic and periodic asymptotics for \(q\)-orthogonal polynomials. (English) Zbl 1109.33025 Int. Math. Res. Not. 2006, No. 23, Article ID 83274, 33 p. (2006). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 41A60 11F27 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Int. Math. Res. Not. 2006, No. 23, Article ID 83274, 33 p. (2006; Zbl 1109.33025) Full Text: DOI
Ismail, Mourad E. H.; Li, Xin Orthogonal polynomials and Ramanujan’s \(q\)-continued fractions. (English) Zbl 1107.33010 ETNA, Electron. Trans. Numer. Anal. 25, 158-165 (2006). MSC: 33C47 11A55 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{X. Li}, ETNA, Electron. Trans. Numer. Anal. 25, 158--165 (2006; Zbl 1107.33010) Full Text: EuDML Link
Chiang, Yik-Man; Ismail, Mourad E. H. On value distribution theory of second order periodic ODEs, special functions and orthogonal polynomials. (English) Zbl 1115.34081 Can. J. Math. 58, No. 4, 726-767 (2006). Reviewer: Kazuya Tohge (Kanazawa) MSC: 34M10 33C15 33C47 PDFBibTeX XMLCite \textit{Y.-M. Chiang} and \textit{M. E. H. Ismail}, Can. J. Math. 58, No. 4, 726--767 (2006; Zbl 1115.34081) Full Text: DOI
Ismail, Mourad E. H.; Stanton, Dennis Ramanujan continued fractions via orthogonal polynomials. (English) Zbl 1103.11003 Adv. Math. 203, No. 1, 170-193 (2006). Reviewer: Takao Komatsu (Hirosaki) MSC: 11A55 40A15 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{D. Stanton}, Adv. Math. 203, No. 1, 170--193 (2006; Zbl 1103.11003) Full Text: DOI
Christiansen, Jacob S.; Ismail, Mourad E. H. A moment problem and a family of integral evaluations. (English) Zbl 1089.33016 Trans. Am. Math. Soc. 358, No. 9, 4071-4097 (2006). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 44A60 47B34 PDFBibTeX XMLCite \textit{J. S. Christiansen} and \textit{M. E. H. Ismail}, Trans. Am. Math. Soc. 358, No. 9, 4071--4097 (2006; Zbl 1089.33016) Full Text: DOI
Duran, Antonio J.; Ismail, Mourad E. H. Differential coefficients of orthogonal matrix polynomials. (English) Zbl 1100.42017 J. Comput. Appl. Math. 190, No. 1-2, 424-436 (2006). Reviewer: Andrei Martínez Finkelshtein (Almeria) MSC: 42C05 33E30 39B42 PDFBibTeX XMLCite \textit{A. J. Duran} and \textit{M. E. H. Ismail}, J. Comput. Appl. Math. 190, No. 1--2, 424--436 (2006; Zbl 1100.42017) Full Text: DOI
Ismail, Mourad E. H. [Van Assche, Walter] Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. (English) Zbl 1082.42016 Encyclopedia of Mathematics and its Applications 98. Cambridge: Cambridge University Press (ISBN 0-521-78201-5). xviii, 706 p. (2005). Reviewer: Leonid Golinskii (Kharkov) MSC: 42C05 42C15 33D80 33C45 33C50 33D45 42-02 33-02 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Cambridge: Cambridge University Press (2005; Zbl 1082.42016)
Ismail, Mourad E. H. Asymptotics of \(q\)-orthogonal polynomials and a \(q\)-Airy function. (English) Zbl 1072.33014 Int. Math. Res. Not. 2005, No. 18, 1063-1088 (2005). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 33D15 33C10 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Int. Math. Res. Not. 2005, No. 18, 1063--1088 (2005; Zbl 1072.33014) Full Text: DOI
Ismail, Mourad E. H. Determinants with orthogonal polynomial entries. (English) Zbl 1083.15011 J. Comput. Appl. Math. 178, No. 1-2, 255-266 (2005). Reviewer: Fuad Kittaneh (Amman) MSC: 15A15 42A70 42C05 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, J. Comput. Appl. Math. 178, No. 1--2, 255--266 (2005; Zbl 1083.15011) Full Text: DOI
Chen, Yang; Ismail, Mourad Jacobi polynomials from compatibility conditions. (English) Zbl 1057.33004 Proc. Am. Math. Soc. 133, No. 2, 465-472 (2005). Reviewer: Leonid Golinskii (Kharkov) MSC: 33C45 42C05 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{M. Ismail}, Proc. Am. Math. Soc. 133, No. 2, 465--472 (2005; Zbl 1057.33004) Full Text: DOI arXiv
Bryc, Wlodzimierz; Ismail, Mourad Approximation Operators, Exponential, q-Exponential, and Free Exponential Families. arXiv:math/0512224 Preprint, arXiv:math/0512224 [math.ST] (2005). MSC: 62E10 41A35 44A10 33C45 BibTeX Cite \textit{W. Bryc} and \textit{M. Ismail}, ``Approximation Operators, Exponential, q-Exponential, and Free Exponential Families'', Preprint, arXiv:math/0512224 [math.ST] (2005) Full Text: arXiv
Ismail, Mourad E. H. Lectures on orthogonal polynomials. (English) Zbl 1121.33009 Chen, Hua (ed.) et al., Differential equations and asymptotic theory in mathematical physics. Lectures from the conference, Wuhan University, Hubei, China, October 20–29, 2003. Hackensack, NJ: World Scientific (ISBN 981-256-055-6/hbk). Series in Analysis 2, 1-43 (2004). MSC: 33C45 33-02 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Ser. Anal. 2, 1--43 (2004; Zbl 1121.33009)
Ismail, Mourad E. H.; Nikolova, Inna; Simeonov, Plamen Difference equations and discriminants for discrete orthogonal polynomials. (English) Zbl 1081.33014 Ramanujan J. 8, No. 4, 475-502 (2004). Reviewer: Qiu-Ming Luo (Jiaozuo) MSC: 33C45 33D45 39A10 PDFBibTeX XMLCite \textit{M. E. H. Ismail} et al., Ramanujan J. 8, No. 4, 475--502 (2004; Zbl 1081.33014) Full Text: DOI
Ismail, M. E. H.; Lin, S. S.; Roan, S. S. Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems. arXiv:math-ph/0407033 Preprint, arXiv:math-ph/0407033 [math-ph] (2004). MSC: 33C45 33D45 39A13 BibTeX Cite \textit{M. E. H. Ismail} et al., ``Bethe Ansatz Equations of XXZ Model and q-Sturm-Liouville Problems'', Preprint, arXiv:math-ph/0407033 [math-ph] (2004) Full Text: arXiv
Ismail, Mourad E. H. A generalization of a theorem of Bochner. (English) Zbl 1043.33009 J. Comput. Appl. Math. 159, No. 2, 319-324 (2003). Reviewer: Axel Riese (Linz) MSC: 33D45 33C45 39A70 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, J. Comput. Appl. Math. 159, No. 2, 319--324 (2003; Zbl 1043.33009) Full Text: DOI
Ismail, Mourad E. H. Difference equations and quantized discriminants for \(q\)-orthogonal polynomials. (English) Zbl 1032.33012 Adv. Appl. Math. 30, No. 3, 562-589 (2003). Reviewer: Youssef Ben Cheikh (Monastir) MSC: 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, Adv. Appl. Math. 30, No. 3, 562--589 (2003; Zbl 1032.33012) Full Text: DOI
Ismail, M. E. H.; Stanton, D. Tribasic integrals and identities of Rogers-Ramanujan type. (English) Zbl 1033.33012 Trans. Am. Math. Soc. 355, No. 10, 4061-4091 (2003). Reviewer: Shaun Cooper (Auckland) MSC: 33D45 33E20 05A17 11P99 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{D. Stanton}, Trans. Am. Math. Soc. 355, No. 10, 4061--4091 (2003; Zbl 1033.33012) Full Text: DOI
Ismail, Mourad E. H. Remarks on ”Differential equation of Appell polynomials…”. (English) Zbl 1033.33006 J. Comput. Appl. Math. 154, No. 1, 243-245 (2003). MSC: 33C65 33C45 33E20 PDFBibTeX XMLCite \textit{M. E. H. Ismail}, J. Comput. Appl. Math. 154, No. 1, 243--245 (2003; Zbl 1033.33006) Full Text: DOI
Ismail, Mourad E. H.; Stanton, Dennis Applications of \(q\)-Taylor theorems. (English) Zbl 1024.33012 J. Comput. Appl. Math. 153, No. 1-2, 259-272 (2003). Reviewer: Wolfram Koepf (Kassel) MSC: 33D15 33D45 41A58 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{D. Stanton}, J. Comput. Appl. Math. 153, No. 1--2, 259--272 (2003; Zbl 1024.33012) Full Text: DOI
Ismail, Mourad E. H.; Rahman, Mizan An inverse to the Askey-Wilson operator. (English) Zbl 1069.33017 Rocky Mt. J. Math. 32, No. 2, 657-678 (2002). MSC: 33D15 33D45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{M. Rahman}, Rocky Mt. J. Math. 32, No. 2, 657--678 (2002; Zbl 1069.33017) Full Text: DOI Link
Berg, Christian; Chen, Yang; Ismail, Mourad E. H. Small eigenvalues of large Hankel matrices: The indeterminate case. (English) Zbl 1018.47020 Math. Scand. 91, No. 1, 67-81 (2002). Reviewer: Michal Zajac (Bratislava) MSC: 47B35 44A60 PDFBibTeX XMLCite \textit{C. Berg} et al., Math. Scand. 91, No. 1, 67--81 (2002; Zbl 1018.47020) Full Text: DOI arXiv
Chiang, Yik-Man; Ismail, Mourad E. H. Complex oscillation theory and special functions. (English) Zbl 1054.34140 C. R. Math. Acad. Sci., Soc. R. Can. 24, No. 3, 117-123 (2002). Reviewer: Zhongqiu Ye (Nanchang) MSC: 34M10 33C47 PDFBibTeX XMLCite \textit{Y.-M. Chiang} and \textit{M. E. H. Ismail}, C. R. Math. Acad. Sci., Soc. R. Can. 24, No. 3, 117--123 (2002; Zbl 1054.34140)
Ismail, Mourad E. H.; Stanton, Dennis \(q\)-integral and moment representations for \(q\)-orthogonal polynomials. (English) Zbl 1009.33015 Can. J. Math. 54, No. 4, 709-735 (2002). Reviewer: Roelof Koekoek (Delft) MSC: 33D45 30E05 33D15 33C45 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{D. Stanton}, Can. J. Math. 54, No. 4, 709--735 (2002; Zbl 1009.33015) Full Text: DOI
Ismail, Mourad E. H.; Rahman, Mizan Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials. (English) Zbl 0997.33008 J. Approximation Theory 114, No. 2, 269-307 (2002). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 05A30 26A33 39A13 33D15 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{M. Rahman}, J. Approx. Theory 114, No. 2, 269--307 (2002; Zbl 0997.33008) Full Text: DOI
Muttalib, K. A.; Chen, Y.; Ismail, M. E. H. \(q\)-random matrix ensembles. (English) Zbl 1069.82500 Garvan, Frank G. (ed.) et al., Symbolic computation, number theory, special functions, physics and combinatorics. Proceedings of the conference, Gainesville, FL, USA, November 11–13, 1999. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0101-0/hbk). Dev. Math. 4, 199-221 (2001). MSC: 82B31 33D45 PDFBibTeX XMLCite \textit{K. A. Muttalib} et al., Dev. Math. 4, 199--221 (2001; Zbl 1069.82500) Full Text: arXiv