On contiguity relations of the confluent hypergeometric systems

On the confluent hypergeometric function coming from the Pareto distribution

Making use of the confluent hypergeometric function we can obtain the Laplace-Stieltje transform of the Pareto distribution in the following form ζ(s) = hU(1; 1− h; s) = 1F1(1; 1− h; s)− Γ(1− h)s1F1(1 + h; 1 + h; s). About this transform, we obtain an identity, Γ(1 + h)|U(1, 1− h, s)|2 = ∫ ∞ 0 ∫ ∞ 0 λhe−λ−y |λ+ s|2 + λy 2000 Mathematical Subject Classification: 33C15, 60E07

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...

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

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 ...

Properties of the Bivariate Confluent Hypergeometric Function Kind 1 Distribution

The bivariate confluent hypergeometric function kind 1 distribution is defined by the probability density function proportional to x1 1 x2 2 1 F1(α; β; −x1 − x2). In this article, we study several properties of this distribution and derive density functions of X1/X2, X1/(X1 + X2), X1 + X2 and 2 √ X1X2. The density function of 2 √ X1X2 is represented in terms of modified Bessel function of the s...