リチャード・アスキーのソースを表示

{{Expand English|Richard Askey|date=2019-10}}
[[File:Richard Askey.jpg|thumb|リチャード・アスキー（1977年）]]
'''リチャード・アスキー''' (Richard Askey、[[1933年]][[6月4日]] - [[2019年]][[10月9日]]) は、[[アメリカ合衆国]]の数学者。専門は、[[特殊関数]]・[[直交多項式]]。

==主な業績==
*[[アスキースキーム]]<ref>Koekoek, R., & Swarttouw, R. F. (1996). The Askey-scheme of hypergeometric orthogonal polynomials and its <math>q</math>-analogue. arXiv preprint math/9602214.</ref>
*[[アスキー＝ギャスパー不等式]]
*[[:en:Askey–Wilson polynomials]]
*[[:en:Rogers-Askey-Ismail polynomial|Rogers-Askey-Ismail 多項式]]
*Askey-Wilson 積分<ref>Ismail, M. E., Stanton, D., & Viennot, G. (1987). The combinatorics of <math>q</math>-Hermite polynomials and the Askey—Wilson integral. European Journal of Combinatorics, 8(4), 379-392.</ref><ref>Gustafson, R. A. (1994). Some q-Beta Integrals on SU(n) and Sp(n) That Generalize the Askey–Wilson and Nasrallah–Rahman Integrals. SIAM Journal on Mathematical Analysis, 25(2), 441-449.</ref><ref>Ito, M. (2006). Askey–Wilson type integrals associated with root systems. The Ramanujan Journal, 12(1), 131-151.</ref><ref>Cao, J., & Niu, D. W. (2017). <math>q</math>-difference equations for Askey–Wilson type integrals via <math>q</math>-polynomials. Journal of Mathematical Analysis and Applications, 452(2), 830-845.</ref><ref>Wei, C., Wang, X., & Yan, Q. (2015). Generalizations of Ramanujan’s reciprocity formula and the Askey–Wilson integral. The Ramanujan Journal, 37(1), 203-217.</ref>
*Andrews-Askey 積分<ref>Liu, Z. G. (2016). Extensions of Ramanujan's reciprocity theorem and the Andrews–Askey integral. Journal of Mathematical Analysis and Applications, 443(2), 1110-1129.</ref>

==著書==

* Richard Askey, Orthogonal polynomials and special functions, [[SIAM (学会)|SIAM]], 1975.
* Askey, R., & Ismail, M. (1984). Recurrence relations, continued fractions and orthogonal polynomials. [[アメリカ数学会|American Mathematical Society]].
* Askey, R., & Wilson, J. A. (1985). Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. [[アメリカ数学会|American Mathematical Society]].
* George E. Andrews, Richard Askey, and Ranjan Roy, Special functions, Encyclopedia of Mathematics and Its Applications, [[:en:Cambridge University Press]], 1999.

==代表的な論文==

===共著===
* Askey, R., & Gasper, G. (1977). Convolution structures for Laguerre polynomials. Journal d'Analyse Mathématique, 31(1), 48-68.
* Askey, R., & Wilson, J. (1979). A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. SIAM Journal on Mathematical Analysis, 10(5), 1008-1016.
* Askey, R., & Ismail, M. E. (1979). The Very Well Poised <math>_6\psi_6</math>. Proceedings of the American Mathematical Society, 218-222.
* Askey, R., & Wilson, J. (1982). A set of hypergeometric orthogonal polynomials. SIAM Journal on Mathematical Analysis, 13(4), 651-655.
* Askey, R., Koornwinder, T. H., & Rahman, M. (1986). An Integral of Products of Ultraspherical Functions and a <math>q</math>-Extension. Journal of the London Mathematical Society, 2(1), 133-148.
* Askey, R., & Roy, R. (1986). More <math>q</math>-beta integrals. The Rocky Mountain Journal of Mathematics, 365-372.
* Askey, R. A., Rahman, M., & Suslov, S. (1996). On a general q-Fourier transformation with nonsymmetric kernels. [[:en:Journal of Computational and Applied Mathematics]], 68(1-2), 25-55.
===単著===
* Askey, R. (1978). The <math>q</math>-gamma and <math>q</math>-beta functions. Applicable Analysis, 8(2), 125-141.
* Askey, R. (1980). Ramanujan's extensions of the gamma and beta functions. The American Mathematical Monthly, 87(5), 346-359.
* Askey, R. (1981). A <math>q</math>-extension of Cauchy's form of the beta integral. The Quarterly Journal of Mathematics, 32(3), 255-266.
* Askey, R. (1986). Limits of some <math>q</math>-Laguerre polynomials. Journal of Approximation Theory, 46(3), 213-216.

==出典==

{{reflist}}

==主な共著者==

*[[ワリード・アルサラム]]
*[[ジョージ・アンドリューズ]]
*[[ジョージ・ギャスパー]]
*[[ムーラッド・イスマイル]]
*[[ミザン・ラーマン]]

==外部リンク==
* [http://staff.science.uva.nl/~thk/pictures/Askey80.html Photo gallery on the occasion of Dick Askey's 80th.]
* {{MathGenealogy|id=8039}}
* {{ResearchGate|Richard_Askey}}
* {{DBLP|name=Richard Askey}}
{{mathematician-stub}}

{{authority control}}
{{DEFAULTSORT:あすきい りちやあと}}
[[Category:数学に関する記事]]
[[Category:20世紀の数学者|330604]]
[[Category:アメリカ合衆国の数学者]]
[[Category:特殊関数]]
[[Category:直交多項式]]
[[Category:アメリカ芸術科学アカデミー会員]]
[[Category:米国科学アカデミー会員]]
[[Category:アメリカ数学会フェロー]]
[[Category:SIAMフェロー]]
[[Category:ミズーリ州の科学者]]
[[Category:ミズーリ州の数学者]]
[[Category:1933年生]]
[[Category:2019年没]]