Recurrence relations for discrete hypergeometric functions

À La Carte Recurrence Relations for Continuous and Discrete Hypergeometric Functions

We show how, using the constructive approach for special functions introduced by Nikiforov and Uvarov, one can obtain recurrence relations for the hypergeometric-type functions not only for the continuous case but also for the discrete and q-linear cases, respectively. Some applications in Quantum Physics are discussed. 2000 Mathematics Subject Classification: 33C45, 33D45

Recurrence relations for orthogonal rational functions

It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arb...

Recurrence Relations and Generating Functions

GG-functions and their relations to A-hypergeometric functions

In [1] I.M.Gelfand introduced the conception of hypergeometric functions, associated with the Grassmanian Gk,n of k-dimensional subspaces in C . The class of these functions includes many classical hypergeometric functions as particular cases. Series of consequent papers of I.M.Gelfand and his coathors ([2]–[6]) are devoted to the theory of these functions. In particular, the paper [4] is devot...

Twisted period relations associated with con uent hypergeometric functions

1 Introduction Formulas of intersection numbers were given in [1] and [4] for twisted de-Rham cohomology groups and twisted homology groups dened by the connection r ! = d + ! associated with a 1-form ! with simple poles on the projective line P. In this paper, we present a denition of intersection pair-ing and a formula of intersection numbers between twisted homology groups associated with a ...