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Asymptotic expansions and inequalities for hypergeometric function
Author(s) -
Ponnusamy S.,
Vuorinen M.
Publication year - 1997
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300012602
Subject(s) - mathematics , confluent hypergeometric function , generalized hypergeometric function , basic hypergeometric series , hypergeometric function , hypergeometric function of a matrix argument , ramanujan's sum , pure mathematics , bilateral hypergeometric series , function (biology) , lauricella hypergeometric series , zero (linguistics) , hypergeometric distribution , gaussian , hypergeometric identity , linguistics , philosophy , physics , quantum mechanics , evolutionary biology , biology
Ramanujan's work on the asymptotic behaviour of the hypergeometric function has been recently refined to the zero‐balanced Gaussian hypergeometric function F ( a , b ; a + b ; x ) as x →1. We extend these results for F ( a , b ; c ; x ) when a , b , c >0 and c < a + b .
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