Stokes Matrices for Confluent Hypergeometric Equations

Computation of the Stokes Multipliers of Okubo’s Confluent Hypergeometric System

The Stokes multipliers of Okubo’s confluent hypergeometric system can, in general, not be expressed in closed form using known special functions. Instead they may themselves be regarded as highly interesting new functions of the system’s parameters. In this article we study their dependence on the eigenvalues of the leading term. Doing so, we obtain several interesting representations in terms ...

Solution of Some Integral Equations Involving Confluent k-Hypergeometric Functions

The principle aim of this research article is to investigate the properties of k-fractional integration introduced and defined by Mubeen and Habibullah [1], and secondly to solve the integral equation of the form             1 1 0 , ; d , ; k x k k x t g x F t x f t k                t t 0, 0, 0,0 k x , for          , where     1 1 , ; , ; k F x k     ...

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

Nonlinear Difference Equations and Stokes Matrices

We study one scalar holomorphic function of finitely many complex variables which, under the assumption that one of the two coefficient matrices has all distinct eigenvalues, allows to calculate the Stokes multipliers of Okubo’s confluent hypergeometric system. Many properties of this function, including a nonlinear functional equation, are obtained. An open question is whether the function is ...

Asymptotic Representations of Confluent Hypergeometric Functions.

I A more general theory will result if in the place of R we employ an abstract normed ring. s We use the symbols =, ... ... in more than one sense. No confusion need arise as tie context makes clear the meaning of each such symbol. It is worth while to mention here that the relation of equality = for E1 as well as for E2 is not an independent primitive idea; for, an equivalent set of postulates...