Another $q$-extension of the beta function
Authors: George E. Andrews and Richard Askey
Journal: Proc. Amer. Math. Soc. 81 (1981), 97-100
MSC: Primary 33A15
MathSciNet review: 589145
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Abstract: Another $q$-extension of the beta function is given. This one has a special case that is a symmetric extension of the symmetric beta distribution.
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- Jacques Labelle, Tableau d’Askey, Orthogonal polynomials and applications (Bar-le-Duc, 1984) Lecture Notes in Math., vol. 1171, Springer, Berlin, 1985, pp. xxxvi–xxxvii (French). MR 838967
- Richard Askey, Ramanujan’s extensions of the gamma and beta functions, Amer. Math. Monthly 87 (1980), no. 5, 346–359. MR 567718, DOI https://doi.org/10.2307/2321202
- Richard Askey and James Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985), no. 319, iv+55. MR 783216, DOI https://doi.org/10.1090/memo/0319
G. E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley, Reading, Mass., 1976.
G. E. Andrews and R. Askey, $q$-analogues of the classical orthogonal polynomials and applications (to appear).
R. Askey, Ramanujan’s extensions of the gamma and beta functions, Amer. Math. Monthly 87 (1980), 346-359.
R. Askey and J. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials (to appear).
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Keywords: Beta function, <IMG WIDTH="15" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$q$">-binomial theorem, basic hypergeometric functions
Article copyright: © Copyright 1981 American Mathematical Society