Results 191 to 200 of about 6,079,712 (233)

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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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

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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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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Further results on generalized hypergeometric functions

Applied Mathematics and Computation, 2003
This paper is a sequel to a recent work of \textit{N. Virchenko}, \textit{S. L. Kalla} and \textit{A. Al-Zamel} [Integral Transforms Spec Funct. 12, 89-100 (2001; Zbl 1026.33006)] on a generalized hypergeometric function represented in the following integral form: \[ _2R_1(a,b;c; \tau;z)= {\Gamma(c) \over\Gamma (b)\Gamma (c-b)}\int^1_0 t^{b-1} (1-t)^{c-
Leda Galue, A. Al-Zamel, Shyam L. Kalla
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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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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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Classes of analytic functions associated with the generalized hypergeometric function

Applied Mathematics and Computation, 1999
Using the generalized hypergeometric function, the authors introduce and study a class of analytic functions with negative coefficients. Coefficients estimates, distortion theorems, extreme points, and the radii of convexity and starlikeness for this class are given. Relevant connections of these results with those in several earlier investigations are
Jacek Dziok, H. M. Srivastava 0001
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A new generalization of q-hypergeometric function

Bollettino dell'Unione Matematica Italiana, 2015
The author introduces a so-called \(q\)-\(\ell\)-\(\Psi\) function by \[ \Psi\left[\begin{matrix} a; & b; & q; & z\\ c; & \left( d:\ell\right) ; & & \end{matrix} \right] =\sum_{n=0}^{\infty}\frac{\left( a;q\right) _{n}\left( b;q\right) _{n}}{\left( c;q\right) _{n}\left( d;q\right) _{n}^{\ell n}}\frac{z^{n} }{\left( q;q\right) _{n}}, \] where ...
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On the Hankel Transform of Generalized Hypergeometric Functions

Journal of the London Mathematical Society, 1946
Not ...
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