Asymptotic Representations of 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...

On modified asymptotic series involving confluent hypergeometric functions

A modification of standard Poincaré asymptotic expansions for functions defined by means of Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptotic expansion involves confluent hypergeometric functions ...

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

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     ...

New Laplace transforms of Kummer's confluent hypergeometric functions

In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function 1F1(a; b; x) by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical p...