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.

It is shown that analytically soluble bound states of the Schrodinger equation for a large class of systems relevant to atomic and molecular physics can be obtained by means of the Laplace transform of the confluent ...

We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear ...

We study an energy-dependent potential related to the Rosen-Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrodinger operator in terms of a class of functions associated to a ...

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 ...

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 ...

The derivatives of any order of the general hypergeometric function pFq(a1.....ap; b1.....bq;z) with respect to the parameters a; or bj are expressed, in compact form, in terms of generalizations of multivariable Kampe de ...