Abstract
In this paper, we describe some reduction formulae for Gaussâ hypergeometric function and Fox-Wright hypergeometric function associated with suitable convergence conditions using series rearrangement technique.
Highlights
Introduction and Basic NotationsIn the present paper, we shall use the following standard notations:N := {1, 2,3, },N0 := {0,1, 2,3, } = N ∪{0} Z0− := {0, −1, −2, −3, }, Z− := {−1, −2, −3, } = Z0− \ {0} and Z = (Z0− ∪ Z)
In this paper, we describe some reduction formulae for Gauss’ hypergeometric function and Fox-Wright hypergeometric function associated with suitable convergence conditions using series rearrangement technique
Denotes the set of real numbers, R+ denotes the set of positive real numbers and C denotes the set of complex numbers
Summary
We shall use the following standard notations:. N := {1, 2,3, },N0 := {0,1, 2,3, } = N ∪{0} Z0− := {0, −1, −2, −3, }, Z− := {−1, −2, −3, } = Z0− \ {0} and Z = (Z0− ∪ Z). Case(I): When contour (L) is a left loop beginning and ending at −∞ , p Ψq given by (1.4) or (1.6) holds the following convergence conditions i) when ∆* > −1, 0 1 .
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