Septic analogues of the Rogers-Ramanujan functions
Septic theta function identities in Ramanujan's lost notebook
Sequences of definite integrals, factorials and double factorials.
Series and iterations for 1/π
Series and recurrence relations for Meijer's G-function
Séries de -factorielles, opérateurs aux -différences et confluence
Séries d'Eisenstein et transcendance
Séries hypergéométriques et irrationalité des valeurs de la fonction zêta de Riemann
Nous effectuons un survol des résultats connus sur la nature diophantienne des valeurs de la fonction zêta de Riemann aux entiers. Nous mettons en particulier l’accent sur le rôle important des séries hypergéométriques dans les démonstrations de l’irrationalité de et d’une infinité des nombres .
Séries hypergéométriques multiples et polyzêtas
Nous décrivons un algorithme théorique et effectif permettant de démontrer que des séries et intégrales hypergéométriques multiples relativement générales se décomposent en combinaisons linéaires à coefficients rationnels de polyzêtas.
Several properties of generalized Fox's H-functions and their applications
Several -series identities from the Euler expansions of and
In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two -series identities obtained by the Euler expansions of and . Several -series identities are obtained involving a -series identity in Ramanujan’s Lost Notebook.
Sharp Becker-Stark-type inequalities for Bessel functions.
Sidon sets and Riesz sets for some measure algebras on the disk
Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.
Siebzehntheilung des Lemniscatenumfangs durch alleinige Anwendung von Lineal und Cirkel.
Signed words and permutations. III: The MacMahon Verfahren.
Singular eigenfunctions of Calogero-Sutherland type systems and how to transform them into regular ones.
Singular values, Ramanujan modular equations, and Landen transformations
A new connection between geometric function theory and number theory is derived from Ramanujan’s work on modular equations. This connection involves the function recurrent in the theory of plane quasiconformal maps. Ramanujan’s modular identities yield numerous new functional identities for for various primes p.
SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions
MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40The paper contains some new formulas involving the Whittaker functions and arising as the values of some double integrals, which are invariant with respect to the representation of the group SO(2; 1).
Sobolev orthogonal polynomials: Interpolation and approximation.
Software for the algorithmic work with orthogonal polynomials and special functions.