A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties ...

A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties ...

We describe the structure of all codimension-2 lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all the partial derivatives of which are nonzero, and which is ...

We discover a deep connection between the Fokker-Planck equation and the hypergeometric differential equation. The same applies to a nonlinear generalization of such equation.

We show that the Schrödinger and Klein-Gordon equations can both be derived from a hypergeometric differential equation. The same applies to non linear generalizations of these equations.

In this work we present a numerical scheme to compute the two-variable hypergeometric function F1(α,β,β′,γ;x,y) of Appell for complex parameters α,β,β′ and γ, and real values of the variables x and y. We implement a set ...

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these ...