IJPAM: Volume 20, No. 3 (2005)

HYPERGEOMETRIC FUNCTIONS AND INFINITE
DIVISIBILITY OF PROBABILITY DISTRIBUTIONS
CONSISTING OF GAMMA FUNCTIONS

Katsuo Takano
Department of Mathematics
Faculty of Science
Ibaraki University
Bunkyo 2-1-1, Mito 310-8512, JAPAN
e-mail: ktaka@mx.ibaraki.ac.jp


Abstract.It is shown that a probability distribution with density function, $C\vert\Gamma (m+ix)\vert^2,$ is an infinitely divisible probability distribution. Here $m$ is a real positive constant and $C$ equals $2^{2m}/\{2\pi\Gamma (2m)\}.$

Received: April 15, 2005

AMS Subject Classification: 30C15, 33C05, 60E07

Key Words and Phrases: hypergeometric series, gamma function, infinitely divisible, probability distributions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 3