Rarefied elliptic hypergeometric functions [PDF]
, 2018 Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a special $n=1$ case,
Spiridonov, V.
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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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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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The c-function expansion of a basic hypergeometric function associated to root systems [PDF]
, 2014 We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by Cherednik in case ...
Gasper +11 more
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Some properties of generalized hypergeometric Appell polynomials [PDF]
, 2020 In this paper, we present a new real-valued Appell-type polynomial family $A_n^{(k)}(m,x), $ every member of which is expressed by mean of a generalized hypergeometric function.
Bedratyuk., L, Luno, N.
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Algebraic A-hypergeometric functions [PDF]
Inventiones mathematicae, 2010 14 pages, 3 figures, research ...
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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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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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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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A (p,q)-extension of Srivastava's triple hypergeometric function HB and its properties [PDF]
, 2019 In this paper, we obtain a (p,q)-extension of Srivastava's triple hypergeometric function HB(⋅), by using the extended Beta function Bp,q(x,y) introduced by Choi et al. (2014).
Dar, S. A., Paris, R. B.
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