A confluent hypergeometric integral equation

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     ...

A new integral solution of the hypergeometric equation

In this work we derive a new integral of the hypergeometric differential equation, valid for arbitrary parameters α, β, γ and which is expressed in terms of indefinite integrals. This leads to new types of relations between F (α, β, γ;x) and its contiguous functions : F (α, β, γ;x) can be related to only one of the functions contiguous to it.These equations enable one to extend the formulae giv...

Integral relations for solutions of the confluent Heun equation

Abstract: Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions. Thirdly, by using one of the integral rel...

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

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...