ムーラッド・イスマイル

ムーラッド・イスマイル (Mourad Ismail, 1944年4月27日 -) は、エジプトの数学者。専門は、特殊関数・直交多項式。

主な業績

• en:Rogers-Askey-Ismail polynomials
• en:Al-Salam-Ismail polynomials
• en:Chihara-Ismail polynomials

主な共同研究者

• 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

著書・解説記事

• Askey, R., & Ismail, M. (1984). Recurrence relations, continued fractions and orthogonal polynomials. American Mathematical Society.
• Ismail, Mourad E. H. (2005), Classical and Quantum Orthogonal Polynomials in One Variable, ISBN 978-0-521-78201-2
• Ismail, M. E., & Zhang, R. (2017). A review of multivariate orthogonal polynomials. Journal of the Egyptian Mathematical Society, 25(2), 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.

代表的な論文

共著

1980年代

• Ismail, M. E., & Wilson, J. A. (1982). Asymptotic and generating relations for the $q$-Jacobi and $_{4}\varphi _{3}$ polynomials. Journal of Approximation Theory, 36(1), 43-54.
• Ismail, M. E., Lorch, L., & Muldoon, M. E. (1986). Completely monotonic functions associated with the gamma function and its $q$-analogues. Journal of Mathematical Analysis and Applications, 116(1), 1-9.
• Bustoz, J., & Ismail, M. E. (1986). On gamma function inequalities. en:Mathematics of Computation, 47(176), 659-667.
• Ismail, M. E., Stanton, D., & Viennot, G. (1987). The combinatorics of $q$-Hermite polynomials and the Askey—Wilson integral. European Journal of Combinatorics, 8(4), 379-392.
• Ismail, M. E., & Muldoon, M. E. (1988). On the variation with respect to a parameter of zeros of Bessel and $q$-Bessel functions. Journal of Mathematical Analysis and Applications, 135(1), 187-207.
• Ismail, M. E., & Stanton, D. (1988). On the Askey-Wilson and Rogers polynomials. Canadian Journal of Mathematics, 40(5), 1025-1045.

1990年代

• Ismail, M. E., & Rahman, M. (1991). The associated Askey-Wilson polynomials. Transactions of the American Mathematical Society, 328(1), 201-237.
• Ismail, M. E., Masson, D. R., & Rahman, M. (1991). Complex weight functions for classical orthogonal polynomials. Canadian Journal of Mathematics, 43(6), 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 (1992): 39-60.
• Ismail, M. E., & Masson, D. R. (1994). $q$-Hermite polynomials, biorthogonal rational functions, and $q$-beta integrals. Transactions of the American Mathematical Society, 346(1), 63-116.
• Ismail, M., & Rahman, M. (1995). Some basic bilateral sums and integrals. Pacific Journal of Mathematics, 170(2), 497-515.
• Ismail, M. E., & Masson, D. R. (1995). Generalized orthogonality and continued fractions. Journal of Approximation Theory, 83(1), 1-40.
• Brown, B. M., & Ismail, M. E. (1995). A right inverse of the Askey-Wilson operator. Proceedings of the American Mathematical Society, 123(7), 2071-2079.
• Chen, Y., & Ismail, M. E. (1997). Ladder operators and differential equations for orthogonal polynomials. Journal of Physics A: Mathematical and General, 30(22), 7817.
• Ismail, M. E., & Stanton, D. (1997). Classical orthogonal polynomials as moments. Canadian Journal of Mathematics, 49(3), 520-542.
• Ismail, M. E., & Rahman, M. (1998). The $q$-Laguerre Polynomials and Related Moment Problems. Journal of Mathematical Analysis and Applications, 218(1), 155-174.
• Ismail, M., Rahman, M., & Stanton, D. (1999). Quadratic $q$-exponentials and connection coefficient problems. Proceedings of the American Mathematical Society, 127(10), 2931-2941.

2000年代

• Ismail, M. E., & Pitman, J. (2000). Algebraic evaluations of some Euler integrals, duplication formulae for Appell's hypergeometric function $F_{1}$, and Brownian variations. Canadian Journal of Mathematics, 52(5), 961-981.
• Ismail, M. E., & Stanton, D. W. (2000). Addition theorems for the $q$-exponential function. Contemporary Mathematics, 254, 235-246.
• Ismail, M. E., Valent, G., & Yoon, G. J. (2001). Some orthogonal polynomials related to elliptic functions. Journal of Approximation Theory, 112(2), 251-278.
• Ismail, M. E., & Stanton, D. (2002). $q$-Integral and moment representations for $q$-orthogonal polynomials. Canadian Journal of Mathematics, 54(4), 709-735.
• Ismail, M. E., & Stanton, D. (2003). Applications of $q$-Taylor theorems. en:Journal of Computational and Applied Mathematics, 153(1-2), 259-272.

2010年代

• Ismail, M., & Simeonov, P. (2015). Complex Hermite polynomials: their combinatorics and integral operators. Proceedings of the American Mathematical Society, 143(4), 1397-1410.
• Genest, V., Ismail, M., Vinet, L., & Zhedanov, A. (2016). Tridiagonalization of the hypergeometric operator and the Racah–Wilson algebra. Proceedings of the American Mathematical Society, 144(10), 4441-4454.
• Ismail, M. E. H., & Zhang, R. (2016). Classes of bivariate orthogonal polynomials. Symmetry, Integrability and Geometry: Methods and Applications, 12(0), 21-37.
• Ismail, M., & Zhang, R. (2017). On some 2D orthogonal $q$-polynomials. Transactions of the American Mathematical Society, 369(10), 6779-6821.
• Ismail, M., & Zhang, R. (2018). $q$-Bessel functions and Rogers-Ramanujan type identities. Proceedings of the American Mathematical Society, 146(9), 3633-3646.

単著

• Ismail, M. E. (1977). A simple proof of Ramanujan's $_{1}\psi _{1}$ sum. Proceedings of the American Mathematical Society, 63(1), 185-186.
• Ismail, M. E. (1981). The basic Bessel functions and polynomials. SIAM Journal on Mathematical Analysis, 12(3), 454-468.
• Ismail, M. E. (1982). Journal of Mathematical Analysis and Applications, 86(1), 1-19.
• Ismail, M. (2016). Analytic properties of complex Hermite polynomials. Transactions of the American Mathematical Society, 368(2), 1189-1210.

外部リンク

• ムーラッド・イスマイル - Mathematics Genealogy Project
• ムーラッド・イスマイルの出版物 - ResearchGate