Results 11 to 20 of about 12,448 (236)
Algebraic transformations of Gauss hypergeometric functions
Funkcialaj Ekvacioj, 2009 This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations.
Vidunas, Raimundas
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On Extensions of Extended Gauss Hypergeometric Function
Communications in Advanced Mathematical Sciences, 2019 The aim of this paper is to introduce a new extensions of extended Gauss hypergeometric function. Certain integral representations, transformation and summation formulas for extended Gauss hypergeometric function are presented and some special cases are ...
Ahmed Ali Atash +2 more
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On the generalized Gauss hypergeometric function
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2008 In this work the (τ, β)-hypergeometric Gauss function is considered, the basic properties of this function are investigated, some applications are given.
N. A. Virchenko
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New Series Expansions of the Gauss Hypergeometric Function [PDF]
Advances in Computational Mathematics, 2013 The Gauss hypergeometric function ${}_2F_1(a,b,c;z)$ can be computed by using the power series in powers of $z, z/(z-1), 1-z, 1/z, 1/(1-z),(z-1)/z$. With these expansions ${}_2F_1(a,b,c;z)$ is not completely computable for all complex values of $z$.
López, José Luis, Temme, Nico M.
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Darboux evaluations of algebraic Gauss hypergeometric functions
Kyushu Journal of Mathematics, 2012 This paper presents explicit expressions for algebraic Gauss hypergeometric functions. We consider solutions of hypergeometric equations with the tetrahedral, octahedral and icosahedral monodromy groups.
Vidunas, Raimundas
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Gauss hypergeometric function and quadratic $R$-matrix algebras
St. Petersburg mathematical journal, 1993 We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit cases and on ...
Koornwinder, Tom H., Kuznetsov, Vadim B.
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DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2011 Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the argument variable.
Raimundas Vidūnas
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Parametric Transformations between the Heun and Gauss Hypergeometric Functions
Funkcialaj Ekvacioj, 2013 The hypergeometric and Heun functions are classical special functions. Transformation formulas between them are commonly induced by pull-back transformations of their differential equations, with respect to some coverings P1-to-P1. This gives expressions of Heun functions in terms of better understood hypergeometric functions. This article presents the
Raimundas Vidunas, Galina Filipuk
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Cumhuriyet Science Journal, 2022 When the literature is examined, it is seen that there are many studies on the generalizations of gamma, beta and hypergeometric functions. In this paper, new types of generalized gamma and beta functions are defined and examined using the Wright ...
Enes Ata, İ. Onur Kıymaz
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TRANSFORMATIONS AND INVARIANTS FOR DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2012 Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums.
Raimundas Vidūnas
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