Ramanujan and hypergeometric and basic hypergeometric series. (English. Russian original) Zbl 0722.33009

Askey, Richard

Russ. Math. Surv. 45, No. 1, 37-86 (1990); translation from Usp. Mat. Nauk 45, No. 1(271), 33-76 (1990).

This paper is a Russian translation of a paper which first appeared in “Ramanujan International Symposium in Analysis”, ed. N. K. Thakare, MacMillan India, Delhi, 1-83 (1989). The original was a summary of much of what was known on hypergeometric and basic hypergeometric series when Ramanujan started to study them about 1905, his contributions, and a little on their impact on the development of mathematics in this century. In addition some material on Ramanujan’s life which was written in the 1910’s and stored first in the Archives of the Madras Port Authority and now in the Indian National Archives in New Delhi is summarized. This paper was an attempt to assess Ramanujan’s significance in one of the many areas to be studied. In the Russian version there is an appendix by the translators, N. M. Atakishiyev and S. K. Suslov, which includes references to the recent work on classical type orthogonal polynomials.

Reviewer: R.Askey

MSC:

33C20	Generalized hypergeometric series, \({}_pF_q\)
33D15	Basic hypergeometric functions in one variable, \({}_r\phi_s\)
33-03	History of special functions
01A55	History of mathematics in the 19th century
01A60	History of mathematics in the 20th century

Keywords:

hypergeometric series; basic hypergeometric series