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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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Two-Sided Inequalities for Generalized Hypergeometric Function
, 2007 We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Inequalities are derived as corollaries of a theorem asserting the monotony of the quotient of two ...
Sitnik, S. M, Karp, D
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Ural Mathematical Journal, 2017 A formula for the non-elementary integral \(\int e^{\lambda x^\alpha} dx\) where \(\alpha\) is real and greater or equal two, is obtained in terms of the confluent hypergeometric function \(_{1}F_1\) by expanding the integrand as a Taylor series.
Victor Nijimbere
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Powers of a hypergeometric function [PDF]
Integral Transforms and Special Functions, 2006 A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.
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A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions
Condensed Matter Physics, 2022 The confluent hypergeometric equation, also known as Kummer's equation, is one of the most important differential equations in physics, chemistry, and engineering. Its two power series solutions are the Kummer function, M(a,b,z), often referred to as the
W. N. Mathews Jr. +3 more
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Hypergeometric functions in arithmetic geometry [PDF]
, 2009 textHypergeometric functions seem to be ubiquitous in mathematics. In this document, we present a couple of ways in which hypergeometric functions appear in arithmetic geometry.
Salerno, Adriana Julia, 1979-
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ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS
Malaysian Journal of Computing, 2021 Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, further generalized extended beta function with some of its properties like summation
Umar Muhammad Abubakar, Saroj Patel
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Contractions of 2D 2nd Order Quantum Superintegrable Systems and the Askey Scheme for Hypergeometric Orthogonal Polynomials [PDF]
, 2013 We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing.
Willard Miller Jr. +8 more
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A Generalised Hypergeometric Function [PDF]
Proceedings of the Edinburgh Mathematical Society, 1956 The hypergeometric function1F(a, b; c; z) is analytic in the domain |arg(−z)| < π, and, when |z| < 1, may be represented by the seriesWhen |z| = 1 in the domain |arg(−z)| <π, this series converges2 to F(a; b; c; z) if R(a+b−c) < 0 (integral values of a, b and c are excluded in the present paper).
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A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms
Journal of Mathematics, 2022 The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new.
Vandana Palsaniya +3 more
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