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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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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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Starlike Hypergeometric Functions [PDF]
Proceedings of the American Mathematical Society, 1961 E. P. Merkes, W. T. Scott
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Inductance and hypergeometric functions
Journal of Computational and Applied Mathematics, 1991 AbstractVector potential and inductances for simple current distributions with rotational symmetry are considered. The approach is in terms of those hypergeometric functions that yield the simplest expressions, rather than complete elliptic integrals. In particular, an integral for the self-inductance of a solenoid of arbitrary thickness and length is ...
Per W. Karlsson
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Hypergeometric Functions for Function Fields
Finite Fields and Their Applications, 1995 AbstractWe introduce and study analogues of hypergeometric functions in the setting of function fields over finite fields. We show analogues of the differential equations, integral representations, transformation formulae, and continued fractions and show how analogues of various special functions and orthogonal polynomials occur as their ...
Dinesh S. Thakur
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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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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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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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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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