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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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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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An application of hypergeometric functions to heat kernels on rectangular and hexagonal tori and a "Weltkonstante"-or-how Ramanujan split temperatures. [PDF]
Ramanujan J, 2021 Faulhuber M.
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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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Some Inequalities of Extended Hypergeometric Functions
Mathematics, 2021 Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent ...
Shilpi Jain +3 more
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On the Algebraic Independence of the Values of Functions Associated with Hypergeometric Functions
Axioms, 2022 Functions that are integrals of products of generalized hypergeometric functions of some kind are considered. The conditions for the representability of these functions as a polynomial in hypergeometric ones are found.
Vasily Gorelov
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Derivatives of any Horn-type hypergeometric functions with respect to their parameters
Nuclear Physics B, 2020 We consider the derivatives of Horn hypergeometric functions of any number of variables with respect to their parameters. The derivative of such a function of n variables is expressed as a Horn hypergeometric series of n+1 infinite summations depending ...
Vladimir V. Bytev, Bernd A. Kniehl
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Three- and four-term recurrence relations for Horn's hypergeometric function $H_4$
Researches in Mathematics, 2022 Three- and four-term recurrence relations for hypergeometric functions of the second order (such as hypergeometric functions of Appell, Horn, etc.) are the starting point for constructing branched continued fraction expansions of the ratios of these ...
R.I. Dmytryshyn, I.-A.V. Lutsiv
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