Univalence of Gaussian and Confluent Hypergeometric Functions

Polynomial series expansions for confluent and Gaussian hypergeometric functions

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions M(a, c; ·) and for Gaussian hypergeometric functions F (a, b; c; ·) are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions M(a, c; ·) and F (a, b; c; ·), in particular, if the parameters are al...

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...

Confluent A-hypergeometric functions and rapid decay homology cycles

We study confluent A-hypergeometric functions introduced by Adolphson [1]. In particular, we give their integral representations by using rapid decay homology cycles of Hien [17] and [18]. The method of toric compactifications introduced in [27] and [31] will be used to prove our main theorem. Moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent A-hype...

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     ...