ムーラッド・イスマイル

ムーラッド・イスマイル  は、エジプトの数学者。専門は、特殊関数・直交多項式。

1. 主な業績
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:en:Rogers-Askey-Ismail polynomials
:en:Al-Salam-Ismail polynomials
:en:Chihara-Ismail polynomials

2. 主な共同研究者
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リチャード・アスキー
ワリード・アルサラム
ミザン・ラーマン

3. 著書・解説記事
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Askey, R., & Ismail, M. . Recurrence relations, continued fractions and orthogonal polynomials. American Mathematical Society.
Ismail, Mourad E. H. , Classical and Quantum Orthogonal Polynomials in One Variable, ISBN 978-0-521-78201-2
Ismail, M. E., & Zhang, R. . A review of multivariate orthogonal polynomials. Journal of the Egyptian Mathematical Society, 25, 91-110.
Encyclopedia of Special Functions: The Askey–Bateman Project, Volume 1: Univariate Orthogonal Polynomials, edited by Mourad E. H. Ismail, published by :en:Cambridge University Press, 2020.

4. 代表的な論文
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4.1. 共著
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4.1.1. 1980年代
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Ismail, M. E., & Wilson, J. A. . Asymptotic and generating relations for the -Jacobi and polynomials. Journal of Approximation Theory, 36, 43-54.
Ismail, M. E., Lorch, L., & Muldoon, M. E. . Completely monotonic functions associated with the gamma function and its -analogues. Journal of Mathematical Analysis and Applications, 116, 1-9.
Bustoz, J., & Ismail, M. E. . On gamma function inequalities. :en:Mathematics of Computation, 47, 659-667.
Ismail, M. E., Stanton, D., & Viennot, G. . The combinatorics of -Hermite polynomials and the Askey—Wilson integral. European Journal of Combinatorics, 8, 379-392.
Ismail, M. E., & Muldoon, M. E. . On the variation with respect to a parameter of zeros of Bessel and -Bessel functions. Journal of Mathematical Analysis and Applications, 135, 187-207.
Ismail, M. E., & Stanton, D. . On the Askey-Wilson and Rogers polynomials. Canadian Journal of Mathematics, 40, 1025-1045.

4.1.2. 1990年代
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Ismail, M. E., & Rahman, M. . The associated Askey-Wilson polynomials. Transactions of the American Mathematical Society, 328, 201-237.
Ismail, M. E., Masson, D. R., & Rahman, M. . Complex weight functions for classical orthogonal polynomials. Canadian Journal of Mathematics, 43, 1294-1308.
Ismail, Mourad EH, and Richard W. Ruedemann. "Relation between polynomials orthogonal on the unit circle with respect to different weights." Journal of Approximation Theory 71, no. 1 : 39-60.
Ismail, M. E., & Masson, D. R. . -Hermite polynomials, biorthogonal rational functions, and -beta integrals. Transactions of the American Mathematical Society, 346, 63-116.
Ismail, M., & Rahman, M. . Some basic bilateral sums and integrals. Pacific Journal of Mathematics, 170, 497-515.
Ismail, M. E., & Masson, D. R. . Generalized orthogonality and continued fractions. Journal of Approximation Theory, 83, 1-40.
Brown, B. M., & Ismail, M. E. . A right inverse of the Askey-Wilson operator. Proceedings of the American Mathematical Society, 123, 2071-2079.
Chen, Y., & Ismail, M. E. . Ladder operators and differential equations for orthogonal polynomials. Journal of Physics A: Mathematical and General, 30, 7817.
Ismail, M. E., & Stanton, D. . Classical orthogonal polynomials as moments. Canadian Journal of Mathematics, 49, 520-542.
Ismail, M. E., & Rahman, M. . The -Laguerre Polynomials and Related Moment Problems. Journal of Mathematical Analysis and Applications, 218, 155-174.
Ismail, M., Rahman, M., & Stanton, D. . Quadratic -exponentials and connection coefficient problems. Proceedings of the American Mathematical Society, 127, 2931-2941.

4.1.3. 2000年代
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Ismail, M. E., & Pitman, J. . Algebraic evaluations of some Euler integrals, duplication formulae for Appell's hypergeometric function , and Brownian variations. Canadian Journal of Mathematics, 52, 961-981.
Ismail, M. E., & Stanton, D. W. . Addition theorems for the -exponential function. Contemporary Mathematics, 254, 235-246.
Ismail, M. E., Valent, G., & Yoon, G. J. . Some orthogonal polynomials related to elliptic functions. Journal of Approximation Theory, 112, 251-278.
Ismail, M. E., & Stanton, D. . -Integral and moment representations for -orthogonal polynomials. Canadian Journal of Mathematics, 54, 709-735.
Ismail, M. E., & Stanton, D. . Applications of -Taylor theorems. :en:Journal of Computational and Applied Mathematics, 153, 259-272.

4.1.4. 2010年代
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Ismail, M., & Simeonov, P. . Complex Hermite polynomials: their combinatorics and integral operators. Proceedings of the American Mathematical Society, 143, 1397-1410.
Genest, V., Ismail, M., Vinet, L., & Zhedanov, A. . Tridiagonalization of the hypergeometric operator and the Racah–Wilson algebra. Proceedings of the American Mathematical Society, 144, 4441-4454.
Ismail, M. E. H., & Zhang, R. . Classes of bivariate orthogonal polynomials. Symmetry, Integrability and Geometry: Methods and Applications, 12, 21-37.
Ismail, M., & Zhang, R. . On some 2D orthogonal -polynomials. Transactions of the American Mathematical Society, 369, 6779-6821.
Ismail, M., & Zhang, R. . -Bessel functions and Rogers-Ramanujan type identities. Proceedings of the American Mathematical Society, 146, 3633-3646.

4.2. 単著
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Ismail, M. E. . A simple proof of Ramanujan's sum. Proceedings of the American Mathematical Society, 63, 185-186.
Ismail, M. E. . The basic Bessel functions and polynomials. SIAM Journal on Mathematical Analysis, 12, 454-468.
Ismail, M. E. . Journal of Mathematical Analysis and Applications, 86, 1-19.
Ismail, M. . Analytic properties of complex Hermite polynomials. Transactions of the American Mathematical Society, 368, 1189-1210.

5. 外部リンク
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