Results 31 to 40 of about 549,355 (294)
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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On Gaussian Hypergeometric Functions of Three Variables: Some New Integral Representations
Journal of Mathematics, 2022 The present paper establishes several new integral representations of the Euler type and Laplace type for some Gauss hypergeometric functions of three variables. The main results are obtained by using the properties of Gamma and beta functions. The novel
Maged G. Bin-Saad +4 more
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Extended Riemann-Liouville type fractional derivative operator with applications
Open Mathematics, 2017 The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind.
Agarwal P., Nieto Juan J., Luo M.-J.
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Monodromy of A-hypergeometric functions [PDF]
Journal für die reine und angewandte Mathematik, 2014 Abstract Using Mellin–Barnes integrals we give a method to compute elements of the monodromy group of an A-hypergeometric system of differential equations. The method works under the assumption that the A-hypergeometric system has a basis of solutions consisting of Mellin–Barnes integrals.
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On digamma series convertible into hypergeometric series [PDF]
arXiv, 2023 Series containing the digamma function arise when calculating the parametric derivatives of the hypergeometric functions and play a role in evaluation of Feynman diagrams. As these series are typically non-hypergeometric, a few instances when they are summable in terms of hypergeometric functions are of importance.
arxiv
Degenerate binomial coefficients and degenerate hypergeometric functions
Advances in Difference Equations, 2020 In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients.
Taekyun Kim +3 more
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Some expansions of hypergeometric functions in series of hypergeometric functions [PDF]
Glasgow Mathematical Journal, 1976 Throughout the present note we abbreviate the set of p parameters a1,…,ap by (ap), with similar interpretations for (bq), etc. Also, by [(ap)]m we mean the product , where [λ]m = Г(λ + m)/ Г(λ), and so on. One of the main results we give here is the expansion formula(1)which is valid, by analytic continuation, when, p,q,r,s,t and u are nonnegative ...
Hari M. Srivastava, Rekha Panda
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Incomplete Caputo fractional derivative operators
Advances in Difference Equations, 2018 The main aim of this paper is to give the definitions of Caputo fractional derivative operators and show their use in the special function theory. For this purpose, we introduce new types of incomplete hypergeometric functions and obtain their integral ...
Mehmet Ali Özarslan, Ceren Ustaoglu
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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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Open Physics, 2022 The main aim of this article is to study a new generalizations of the Gauss hypergeometric matrix and confluent hypergeometric matrix functions by using two-parameter Mittag–Leffler matrix function.
Jain Shilpi +4 more
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