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The integration of generalized hypergeometric functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1966
In the usual notation for generalized hypergeometric functions we letwhereand (a) denotes the sequence of parametersThroughout the present paper we shall suppose that there are A of the a parameters, Bof the b parameters, and so on. Thus ((a))m is to be interpreted asand similar interpretations hold for ((b))m, etc.
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On confluent hypergeometric functions and generalized Bessel functions

Analysis Mathematica, 2017
Conditions are determined on the parameters a and c so that the confluent hypergeometric function Φ(a, c; z) = 1F1(a, c; z) is strongly convex of order 1/2 and the function zΦ(a, c; z) is strongly starlike of order 1/2 in D. Also sufficient conditions are obtained on a and c which ensure that the subordination (c/a)Φ′(a, c; z) ≺ ((1 + z)/(1 − z))1/2 ...
V. Ravichandran, Nisha Bohra
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The integration of generalized hypergeometric functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
Let the generalized hypergeometric function of one variable be denoted bywhere (a)m is the Pochhammer symbol ((1, 3)).
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Generalized Hypergeometric Functions

Mathematics of Computation, 1966
Y. L. L., Lucy Joan Slater
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Confluence expansions of the generalized hypergeometric function

Journal of Mathematical Physics, 2003
By confluencing a subset of upper and lower parameters in the generalized hypergeometric function FQP(a1,,…,aP,c1,…,cQ;z) with the variable z one obtains a lower-order hypergeometric function in the limit when the confluence parameters go to infinity.
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