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Generating functions for the generalized Gauss hypergeometric functions
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. M. Srivastava 0001 +2 more
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GG Functions and their Relations to General Hypergeometric Functions
Letters in Mathematical Physics, 1997The aim of this paper is to give a new approach to hypergeometric functions. According to this approach, hypergeometric functions are defined as solutions of GG-systems which are collections of linear relations for a function \(f(a,\alpha)\) of \(a,\alpha \in {\mathbb C}^N\), its first partial derivative with respect to \(a_i\) and shifts with respect ...
Gelfand, I. M., Graev, M. I.
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Univalent and Starlike Generalized Hypergeometric Functions
Canadian Journal of Mathematics, 1987A 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, 1992A 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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Generating functions of the hypergeometric functions
Journal of Mathematical Physics, 1974The 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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Generalized Hypergeometric Functions
1998Abstract 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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A new generalization of q-hypergeometric function
Bollettino dell'Unione Matematica Italiana, 2015The 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
1990Abstract 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 Functions
200911.1 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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