Results 211 to 220 of about 5,087 (229)

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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Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function

Analysis
Abstract We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol.
Komal Singh Yadav, Bhagwat Sharan, Ashish Verma   +2 more
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Generating functions of the hypergeometric functions

Journal of Mathematical Physics, 1974
The Lie algebra, which was introduced in a previous paper to treat the hypergeometric functions by Lie theory techniques, is used to derive generating functions of the hypergeometric functions. Several generating functions are obtained from the theory of multiplier representations. Weisner's method is also applied, giving another generating function.
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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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HERMITE-PADÉ APPROXIMANTS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS

Russian Academy of Sciences. Sbornik Mathematics, 1995
Let \(\alpha_1, \alpha_2, \dots, \alpha_p\), \(\beta_1, \dots, \beta_q\) with \(p= q+1\) be complex numbers which are neither 0 nor negative integers. Consider the family of contiguous hypergeometric functions \[ \begin{aligned} f_0 (z) &= {}_pF_q \left( {{\alpha_1, \ldots, \alpha_p} \atop {\beta_1, \ldots, \beta_q}} \Biggl|z\right)= \sum^\infty_{n=0} {
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Generalized Hypergeometric Functions

Mathematics of Computation, 1966
Y. L. L., Lucy Joan Slater
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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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GENERALIZED HYPERGEOMETRIC FUNCTIONS

Journal of the London Mathematical Society, 1968
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Generalized Hypergeometric Functions

2018
K Srinivasa Rao, Vasudevan Lakshminarayanan   +1 more
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