Results 31 to 40 of about 2,863,909 (272)
Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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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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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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GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS [PDF]
Honam Mathematical Journal, 2011 Summary: The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas, transform formulas ...
Lee, Dong Myung +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 MathematicsIn 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 +1 more
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Some Generating Functions for a Class of Hypergeometric Polynomials [PDF]
, 2018 This article concerned with some new features for hypergeometric polynomials S-k((alpha, beta)) (x). The results obtained here contain the various families of multilinear and multilateral generating functions, various features and some exceptions for ...
ÖZMEN, NEJLA, Erkus Duman, Esra
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Explicit evaluation of some families of log-sine integrals via the hypergeometric mechanism and their applications [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we present explicit analytical expressions for certain families of log-sine definite integrals: ∫ₒ^2π xᵐ{ln(2sin(x/2))}ⁿdx (m∈ℕ₀, n∈ℕ), expressed in terms of multiple hypergeometric functions of the Kampe de Feriet with arguments ±1 and ...
Shakir Hussain Malik +1 more
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A Study of Generalized Hypergeometric Function and its Applications in Vary Disciplines
Shodh SariElementary functions, Bessel functions, Legendre functions and many other special functions are included in the large family of mathematical functions known as generalized hypergeometric functions.
Mr. Mukesh Kumar Mahala +1 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 +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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