New Conditions for Univalence of Confluent Hypergeometric Function

A Connection Formula for the q-Confluent Hypergeometric Function

We show a connection formula for the q-confluent hypergeometric functions 2φ1(a, b; 0; q, x). Combining our connection formula with Zhang’s connection formula for 2φ0(a, b;−; q, x), we obtain the connection formula for the q-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer’s confluent hypergeometric functions by taking the limit q → 1− of our...

Univalence of Certain Linear Operators Defined by Hypergeometric Function

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...

Univalence of a New General Integral Operator Associated with the q-Hypergeometric Function

Multivariate Generalization of the Confluent Hypergeometric Function Kind 1 Distribution

The confluent hypergeometric function kind 1 distribution with the probability density function pdf proportional to x −11F1 α; β;−x , x > 0 occurs as the distribution of the ratio of independent gamma and beta variables. In this article, a multivariate generalization of this distribution is defined and derived. Several pertinent properties of this multivariate distribution are discussed that sh...