Results 161 to 170 of about 36,153 (203)

Note on generalized hypergeometric function

Integral Transforms and Special Functions, 2013
Virchenko and Rumiantseva [On the generalized associated legendre functions. Fract Cal Appl Anal. 2008;11(2): 175–185] gave another generalization of the hypergeometric function. In this paper, we give integral representations and differentiation formulae of , alongwith relation of with the generalized Mittag–Leffler function [Shukla AK, Prajapati JC ...
Snehal B. Rao, A.K. Shukla
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Geometric Properties of Generalized Hypergeometric Functions

The Ramanujan Journal, 1997
The authors determine conditions on the parameters \(a_j>0\) \((j= 1,2,3)\) and \(b_j> 0\) \((j= 1,2)\) so that the function \[ z{_3F_2}(a_1, a_2,a_3; b_1,b_2; z) \] is univalent in the open unit disk \(U\), \({_3F_2}\) being the Clausenian hypergeometric function.
Ponnusamy, S., Sabapathy, S.
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Univalent and Starlike Generalized Hypergeometric Functions

Canadian Journal of Mathematics, 1987
A single-valued function f(z) is said to be univalent in a domain if it never takes on the same value twice, that is, if f(z1) = f(z2) for implies that z1 = z2. A set is said to be starlike with respect to the line segment joining w0 to every other point lies entirely in . If a function f(z) maps onto a domain that is starlike with respect to w0,
Owa, Shigeyoshi, Srivastava, H. M.
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General hypergeometric functions

Functional Analysis and Its Applications, 1992
A new definition of hypergeometric functions (HF) is given. One considers the manifold \(G^ 0_{n,N}\) of the \(n\)-dimensional subspaces in \(\mathbb{C}^ N\) containing the vector \((1, 1,\dots,1)\) and the vector bundle \(U_{n,N}\) over \(G^ 0_{n,N}\) (that is dual to the tautological vector bundle).
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Generalized Hypergeometric Functions

2009
11.1 Introduction The special properties associated with the hypergeometric and confluent hypergeometric functions have spurred a number of investigations into developing functions even more general than these. Some of this work was done in the nineteenth century by Clausen, Appell, and Lauricella (among others), but much of it has occurred during ...
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Generalized Hypergeometric Functions

1998
Abstract The special properties associated with the hypergeometric and confluent hypergeometric functions have spurred a number of investigations into developing functions even more general than these. Some of this work was done in the nineteenth century by Clausen, Appell, and Lauricella (among others), but much of it has occurred ...
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General Linear Transformations of Hypergeometric Functions

Mathematical Notes, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized hypergeometric functions

1990
Abstract Hypergeometric functions have occupied a significant position in mathematics for over two centuries. This monograph, by one of the foremost experts, is concerned with the Boyarsky principle which expresses the analytical properties of a certain proto-gamma function. Professor Dwork develops here a theory which is broad enough to
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Generalized Hypergeometric Function of Unit Argument

Journal of Mathematical Physics, 1970
Two summation theorems are given for the terminating generalized hypergeometric function pFp−1, for arbitrary p, with certain restrictions on the parameters.
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Zeros of generalized hypergeometric functions

Mathematical Proceedings of the Cambridge Philosophical Society, 1973
In this paper we derive the conditions which have to be satisfied in order to obtain some classes of zeros of the generalized hypergeometric series of the typeThese conditions read:
D'Adda, A., D'Auria, R.
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