Results 31 to 40 of about 2,738,019 (260)
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Hypergeometric Functions over Finite Fields [PDF]
, 2022 Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric ...
Fuselier, Jenny +4 more
core +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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 ...
Srivastava, H. M., Panda, Rekha
openaire +2 more sources
Elliptic hypergeometric functions associated with root systems
, 2020 We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two in essence form an annotated table of the main evaluation and transformation formulas for elliptic hypergeometric integrals ...
Warnaar, Ole, +3 more
core +1 more source
Қарағанды университетінің хабаршысы. Математика сериясыHypergeometric functions are divided into complete and confluent functions. Srivastava and Karlsson were the first to propose a method for constructing the complete set of triple Gaussian hypergeometric series and compiled a table containing definitions
A. Hasanov, T.G. Ergashev, A.R. Ryskan
doaj +1 more source