Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x) [PDF]
, 2012 We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer.
Miller, A. R., Paris, Richard B.
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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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Hypergeometric representation of the two-loop equal mass sunrise diagram [PDF]
, 2006 A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and Appell's F_2 hypergeometric functions is presented.
Appell +46 more
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Further study on the conformable fractional Gauss hypergeometric function
AIMS Mathematics, 2021 This article presents an exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric differential equation (CFGHDE) about the fractional regular singular points
Mahmoud Abul-Ez +2 more
doaj +1 more source
Coherent Excitation of a Two-Level Atom driven by a far off-resonant Classical Field: Analytical Solutions [PDF]
, 2010 We present an analytical treatment of coherent excitation of a Two-Level Atom driven by a far-off resonant classical field. A class of pulse envelope is obtained for which this problem is exactly solvable.
A. M. Dykhne +15 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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Properties of generalized univariate hypergeometric functions [PDF]
, 2006 Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions.
B. Nassrallah +27 more
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Journal of New Theory, 2022 The main objective of this paper is to use the newly proposed $(p,q;l)$-extended beta function to introduce the $(p,q;l)$-extended $τ$-Gauss hypergeometric and the $(p,q;l)$-extended $τ$-confluent hypergeometric functions with some of their properties ...
Umar Muhammad Abubakar
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Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x) [PDF]
, 2010 We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial ...
Miller, A. R., Paris, Richard B.
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Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
Kuwait Journal of Science, 2023 The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper.
Gradimir V. Milovanović +2 more
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