Another -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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Another -extension of the beta function is given. This one has a special case that is a symmetric extension of the symmetric beta distribution.

**[1]**George E. Andrews,*The theory of partitions*, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. Encyclopedia of Mathematics and its Applications, Vol. 2. MR**0557013****[2]**George E. Andrews and Richard Askey,*Classical orthogonal polynomials*, Orthogonal polynomials and applications (Bar-le-Duc, 1984) Lecture Notes in Math., vol. 1171, Springer, Berlin, 1985, pp. 36–62. MR**838970**, 10.1007/BFb0076530**[3]**Richard Askey,*Ramanujan’s extensions of the gamma and beta functions*, Amer. Math. Monthly**87**(1980), no. 5, 346–359. MR**567718**, 10.2307/2321202**[4]**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**, 10.1090/memo/0319

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
33A15

Retrieve articles in all journals with MSC: 33A15

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0589145-1

Keywords:
Beta function,
-binomial theorem,
basic hypergeometric functions

Article copyright:
© Copyright 1981
American Mathematical Society