IJPAM: Volume 21, No. 4 (2005)
PROPERTIES OF SOME SERIES WITH
APPLICATIONS TO THE GAMMA
AND BETA FUNCTIONS
APPLICATIONS TO THE GAMMA
AND BETA FUNCTIONS
Paul Bracken
Department of Mathematics
University of Texas
Edinburg, TX, 78541-2999, USA
e-mail: bracken@panam.edu
Department of Mathematics
University of Texas
Edinburg, TX, 78541-2999, USA
e-mail: bracken@panam.edu
Abstract.A pair of series are studied which have applications
to the theory of the gamma and beta functions. It is
shown that these series can be used to define a related
pair of differentiable functions on the positive real
axis. One of these functions is directly related to
the beta function. The second function is shown to
be related to a beta function type integral. Some
properties of these functions are developed as well.
Received: May 18, 2005
AMS Subject Classification: 33B15, 40G99
Key Words and Phrases: Beta function, Gamma function, infinite series
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 4
