The very well poised . II

Author:
Richard Askey

Journal:
Proc. Amer. Math. Soc. **90** (1984), 575-579

MSC:
Primary 33A35

MathSciNet review:
733409

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A proof of Bailey's sum of the very well poised series is obtained from a simple difference equation and special cases that are easy to evaluate.

**[1]**George E. Andrews,*Applications of basic hypergeometric functions*, SIAM Rev.**16**(1974), 441–484. MR**0352557****[2]**George E. Andrews and Richard Askey,*Enumeration of partitions: the role of Eulerian series and 𝑞-orthogonal polynomials*, Higher combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976), NATO Adv. Study Inst. Ser., Ser. C: Math. Phys. Sci., vol. 31, Reidel, Dordrecht-Boston, Mass., 1977, pp. 3–26. MR**519776****[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,*An elementary evaluation of a beta type integral*, Indian J. Pure Appl. Math.**14**(1983), no. 7, 892–895. MR**714840****[5]**Richard Askey and Mourad E. H. Ismail,*The very well poised ₆𝜓₆*, Proc. Amer. Math. Soc.**77**(1979), no. 2, 218–222. MR**542088**, 10.1090/S0002-9939-1979-0542088-2**[6]**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**[7]**W. N. Bailey,*Series of hypergeometric type which are infinite in both directions*, Quart. J. Math. Oxford Ser.**7**(1936), 105-115.**[8]**Mourad E. H. Ismail,*A simple proof of Ramanujan’s ₁𝜓₁ sum*, Proc. Amer. Math. Soc.**63**(1977), no. 1, 185–186. MR**0508183**, 10.1090/S0002-9939-1977-0508183-7**[9]**Srinivasa Ramanujan,*Notebooks. Vols. 1, 2*, Tata Institute of Fundamental Research, Bombay, 1957. MR**0099904****[10]**L. J. Slater and A. Lakin,*Two proofs of the ₆Ψ₆ summation theorem*, Proc. Edinburgh Math. Soc. (2)**9**(1956), 116–121. MR**0084600**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
33A35

Retrieve articles in all journals with MSC: 33A35

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1984-0733409-8

Keywords:
Basic hypergeometric series

Article copyright:
© Copyright 1984
American Mathematical Society