Saalschützian transforms
Schützenberger groups and Chebyshev polynomials.
Searching for strange hypergeometric identities by sheer brute force.
Selbstadjungierte Differentialoperatoren erster Ordnung in A2 (Co).
Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Semi-orthogonality of a class of the gauss' hypergeometric polynomials
Series and recurrence relations for Meijer's G-function
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
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.
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.
Solution of option pricing equations using orthogonal polynomial expansion
We study both analytic and numerical solutions of option pricing equations using systems of orthogonal polynomials. Using a Galerkin-based method, we solve the parabolic partial differential equation for the Black-Scholes model using Hermite polynomials and for the Heston model using Hermite and Laguerre polynomials. We compare the obtained solutions to existing semi-closed pricing formulas. Special attention is paid to the solution of the Heston model at the boundary with vanishing volatility.
Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics
Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant...
Solution of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels.