Results 21 to 30 of about 98,219 (279)

Decomposition formulas for some quadruple hypergeometric series

Қарағанды университетінің хабаршысы. Математика сериясы, 2020
In the present work, the authors obtained operator identities and decomposition formulas for second order Gauss hypergeometric series of four variables into products containing simpler hypergeometric functions. A Choi–Hasanov method based on the inverse
A.S. Berdyshev, A. Hasanov, A.R. Ryskan
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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, D.P. Gupta, E. Koelink, E. Koelink, E. Koelink, E. M. Rains, F. J. van de Bult, F.J. Bult van de, G. Gasper, G. Letzter, J. V. Stokman, J.F. Diejen van, J.V. Stokman, J.V. Stokman, M. Noumi, M. Put van der, M. Rahman, M.E.H. Ismail, S. Lievens, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, T. Shintani, V.P. Spiridonov, V.P. Spiridonov, W. Groenevelt, Y. Komori   +27 more
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Integral Equations of Fields on the Rotating Black Hole [PDF]

, 1996
It is known that the radial equation of the massless fields with spin around Kerr black holes cannot be solved by special functions. Recently, the analytic solution was obtained by use of the expansion in terms of the special functions and various ...
Carter B., Hisao Suzuki, Takahiro Masuda
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A New Identity for Generalized Hypergeometric Functions and Applications

Axioms, 2019
We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published paper (
Mohammad Masjed-Jamei, Wolfram Koepf
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Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation

, 2000
We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies.
A.Yu. Orlov, Adler, D.M. Scherbin, Dickey, Dryuma, Gelfand, Gerasimov, Graev, Jimbo, Loutsenko, Mikhailov, Miwa, Morozov, Morozov, Nakatsu, Odzijevicz, Orlov, Segal, Takasaki, Takasaki, Takebe, Ueno, Zakharov, Zakharov   +23 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, Mohannad J. S. Shahwan, Jihad A. Younis, Hassen Aydi, Mohamed A. Abd El Salam   +4 more
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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, Dae San Kim, Hyunseok Lee, Jongkyum Kwon   +3 more
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Evaluation of certain families of log-cosine integrals using hypergeometric function approach and applications [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we provide the analytical solutions of the families of certain definite integrals: ∫₀^π xᵐ{ln(2cos(x/2)}ⁿ dx (m∈ℕ₀ and n∈ℕ), in terms of multiple hypergeometric functions of Kampe de Feriet having the arguments ±1 and Riemann zeta ...
Mohammad Idris Qureshi, Shakir Hussain Malik   +1 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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Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions

, 2015
In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of `hypergeometric' algebraic varieties that are higher dimensional analogues of ...
Deines, Alyson, Fuselier, Jenny G., Long, Ling, Swisher, Holly, Tu, Fang-Ting   +4 more
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