Some theorems on the explicit evaluations of singular moduli.
Some theta functions identities associated with the modular equations of degree 5.
Sommation d'une série remarquable
Sonin-type expansions for solutions to a generalized Bessel equation of order and their application.
Sous-groupes analytiques de variétés de groupe
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Special Functions and Infinite-dimensional Representations of Lie Groups.
Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai
The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information...
Special values of multiple gamma functions
We give a Chowla-Selberg type formula that connects a generalization of the eta-function to with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.
Special values of the dilogarithm function
Spécialisation dans les disques singuliers réguliers
Specializations of one-parameter families of polynomials
Let be a number field, and suppose is irreducible over . Using algebraic geometry and group theory, we describe conditions under which the -exceptional set of , i.e. the set of for which the specialized polynomial is -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed , all but finitely many -specializations of the degree generalized Laguerre polynomial are -irreducible and have Galois group . Second, we study specializations...
Spectra of observables in the -oscillator and -analogue of the Fourier transform.
Spectral curves of operators with elliptic coefficients.
Spectral Synthesis on Algebras of Orthogonal Polynomial Series.
Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen
Spherical functions and spectral synthesis
Spherical functions are Fourier transforms of -functions
Spherical functions on a complex classical quantum group
Spherical functions on a family of quantum 3-spheres