Asymptotic behaviour of certain zero-balanced hypergeometric series
In this paper an attempt has been made to give a very simple method of extending certain results of Ramanujan, Evans and Stanton on obtaining the asymptotic behaviour of a class of zero-balanced hypergeometric series. A more recent result of Saigo and Srivastava has also been used to obtain a Ramanujan type of result for a partial sum of a zero-balanced4F3 (1) and similar other partial series of higher order.
KeywordsAsymptotic behaviour zero-balanced hypergeometric series Kampé de Feriet function
Unable to display preview. Download preview PDF.
- Bailey W N, Generalised hypergeometric series,Camb. Tract No. 32, (1935) (London)Google Scholar
- Berndt B C, Ramanujan’s Note Books Part II, (1989) (New York: Springer Verlag)Google Scholar
- Ronald J Evans, Asymptotic expansions for hypergeometric series and related functions,Ramanujan Revisited, Proc. Centenary Conf. Univ. of Illinois at Urbana Campaign (1987) (Ed.) G E Andrewset al (1988) (New York: Academic Press) pp. 537–560Google Scholar
- Ramanujan S, Note books (Tata Inst. Fundamental Research, Bombay) (1957) Vol. IIGoogle Scholar
- Megumi Saigo and Srivastava H M, The behaviour of the zero-balanced hypergeometric seriesp F p-1 near the boundary of its convergence region,Proc. Am. Math. Soc. 11 (1990) 71–76Google Scholar
- Slater L J,Generalised hypergeometric functions, (1966) (Cambridge)Google Scholar