Integrals involving product of Bessel functions and generalized hypergeometric functions.
Integrals of logarithmic and hypergeometric functions
Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. In this paper we explore many relations and explicitly derive closed form representations of integrals of logarithmic, hypergeometric functions and the Lerch phi transcendent in terms of zeta functions and sums of alternating harmonic numbers.
Inversion techniques and combinatorial identities. A unified treatment for the 7f6-series identities.
Inversion techniques and combinatorial identities. Jackson’s -analogue of the Dougall-Dixon theorem and the dual formulae
Irrationalité de valeurs de zêta
Les valeurs aux entiers pairs (strictement positifs) de la fonction de Riemann sont transcendantes, car ce sont des multiples rationnels de puissances de . En revanche, on sait très peu de choses sur la nature arithmétique des , pour entier. Apéry a démontré en 1978 que est irrationnel. Rivoal a prouvé en 2000 qu’une infinité de sont irrationnels, mais sans pouvoir en exhiber aucun autre que . Il existe plusieurs points de vue sur la preuve d’Apéry ; celui des séries hypergéométriques...
-Bessel functions in two variables.
Krätzel Function as a Function of Hypergeometric Type
2000 Mathematics Subject Classification: 33C60, 33C20, 44A15The paper is devoted to the study of the function Zνρ(x) defined for positive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0 for ρ ≤ 0, [...] Such a function was earlier investigated for ρ > 0. Using the Mellin transform of Zνρ(x), we establish its representations in terms of the H-function and extend this function from positive x > 0 to complex z. The results obtained, being different for ρ > 0 and ρ <...
Linear independence of linear forms in polylogarithms
For , , , let be the -th polylogarithm of . We prove that for any non-zero algebraic number such that , the -vector space spanned by has infinite dimension. This result extends a previous one by Rivoal for rational . The main tool is a method introduced by Fischler and Rivoal, which shows the coefficients of the polylogarithms in the relevant series to be the unique solution of a suitable Padé approximation problem.
Linearization relations for the generalized Bedient polynomials of the first and second kinds via their integral representations
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for such familiar classes of hypergeometric polynomials as (for example) the generalized Bedient polynomials of the first and second kinds. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization...
Mellin transforms of Whittaker functions on GL(4, R) and GL(4, C).
On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series
MSC 2010: 33C20
On a generalization of binomial coefficients. (Sur une généralisation des coefficients binomiaux.)
On a new summation formula for basic bilateral hypergeometric series and its applications.
On certain formulas for the multivariable hypergeometric functions.
On convergence of -series involving basic hypergeometric series.
On geometry of fronts in wave propagations
We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
On Hankel Transform of Generalized Mathieu Series
Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20By using integral representations for several Mathieu type series, a number of integral transforms of Hankel type are derived here for general families of Mathieu type series. These results generalize the corresponding ones on the Fourier transforms of Mathieu type series, obtained recently by Elezovic et al. [4], Tomovski [19] and Tomovski and Vu Kim Tuan [20].
On hypergeometric-type generating relations associated with the generalized zeta function.
On Polynomials Associated With Humbert's Polynomials
On -operators and summation of some -series.