Results 151 to 160 of about 3,871 (189)

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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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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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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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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Lie Theory and Generalizations of the Hypergeometric Functions

SIAM Journal on Applied Mathematics, 1973
In this paper we use the differential recurrence relations satisfied by the ${}_2 F_1 $ and their generalizations the${}_p F_q $ and Lauricella functions to associate a Lie algebra (dynamical symmetry algebra) with each of these families of special functions. We demonstrate that the representation theory of the Lie algebras yields a variety of addition
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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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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 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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