Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions

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Abstract

The author aims at finding certain conditions on the parameters a, b and c such that the normalized Gaussian hypergeometric function z F (a, b ; c ; z) given by F (a, b ; c ; z) = underover(∑, n = 0, ∞) frac((a)n (b)n, (c)n (1)n) zn, | z | < 1, is in a certain class of analytic functions. Various results for the particular values of these parameters are deduced. © 2010 Elsevier Ltd. All rights reserved.

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Swaminathan, A. (2010). Sufficient conditions for hypergeometric functions to be in a certain class of analytic functions. Computers and Mathematics with Applications, 59(4), 1578–1583. https://doi.org/10.1016/j.camwa.2009.12.029

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