In praise of an elementary identity of Euler.
Inclusion relations between classes of hypergeometric functions.
Integral and computational representation of summation which extends a Ramanujan's sum
Integral representation of the solutions to Heun's biconfluent equation.
Integral representations and binomial coefficients.
Integrals and polygamma representations for binomial sums.
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...