SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #19  -------------   OP-SF NET 8.6  -------------  November 15, 2001
From: OP-SF NET Editor (
Subject: Book on Incomplete Gamma Functions

[From the web page]

On a Class of Incomplete Gamma Functions with Applications
M. Aslam Chaudhry and Syed M. Zubair,
King Fahd Univ.of Petroleum & Minerals, Saudi Arabia
512 pp.
Chapman & Hall/CRC , 2001, ISBN 1-58488-143-7, $79.95


The subject of special functions is rich and expanding continuously with the
emergence of new problems encountered in engineering and applied science
applications. The development of computational techniques and the rapid
growth in computing power have increased the importance of the special
functions and their formulae for analytic representations. However, problems
remain, particularly in heat conduction, astrophysics, and probability
theory, whose solutions seem to defy even the most general classes of
special functions.

On a Class of Incomplete Gamma Functions with Applications introduces a
class of special functions, developed by the authors, useful in the analytic
study of several heat conduction problems. It presents some basic properties
of these functions, including their recurrence relations, special cases,
asymptotic representations, and integral transform relationships. The
authors explore applications of these generalized functions to problems in
transient heat conduction, special cases of laser sources, and problems
associated with heat transfer in human tissues. They also discuss
applications to astrophysics, probability theory, and other problems in
theory of functions and present a fundamental solution to time-dependent
laser sources with convective-type boundary conditions.

Appendices include an introduction to heat conduction, Fourier conduction, a
table of Laplace transforms, and well-known results regarding the improper
integrals. Filled with tabular and graphical representations for
applications, this monograph offers a unique opportunity to add to your
mathematical toolbox a new and useful class of special functions.

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