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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this ...
Fokko J. van de Bult, Eric M. Rains
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Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions [PDF]
, 2015 In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional analogues of ...
Deines, Alyson +4 more
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Inequalities of extended beta and extended hypergeometric functions [PDF]
Journal of Inequalities and Applications, 2017 We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta ...
Saiful R. Mondal
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Computing hypergeometric functions rigorously [PDF]
ACM Transactions on Mathematical Software, 2016 We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex parameters and ...
Johansson, Fredrik
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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 ...
Vidunas, Raimundas
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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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ϵ-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus
Nuclear Physics B, 2023 We present a new methodology, suitable for implementation on computer, to perform the ϵ-expansion of hypergeometric functions with linear ϵ dependent Pochhammer parameters in any number of variables.
Souvik Bera
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Some $k$-Horn hypergeometric functions and their properties
Journal of New Results in Science, 2023 In the theory of special functions, the $k$-Pochhammer symbol is a generalization of the Pochhammer symbol. With the help of the $k$-Pochhammer symbol, we introduce and study a new generalization of the $k$-Horn hypergeometric functions such as, ${G}_{1}^
Caner Çatak +3 more
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HYPERGEOMETRIC ZETA FUNCTIONS [PDF]
International Journal of Number Theory, 2010 This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers.
Hassen, Abdul, Nguyen, Hieu D.
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International Journal of Mathematics for Industry, 2023 Fractional kinetic equations are of immense importance in describing and solving numerous intriguing problems of physics and astrophysics. Inequalities are important topics in special functions.
Ankita Chandola, Rupakshi Mishra Pandey
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