## OP-SF WEB

### Extract from OP-SF NET

Topic #9 ------------ OP-SF NET 4.5 ------------ September 15, 1997
~~~~~~~~~~~~~
From: OP-SF Editor (thk@wins.uva.nl)
Subject: Book on Mehler-Fock type transform
The following announcement was found on the web site:
http://www.awl-he.com/advmaths/titles/367.html
Pitman Research Notes in Mathematics Series 367
Integral Expansions Related to Mehler-Fock Type Transforms
B N Mandal and Nanigopal Mandal
An important class of integral expansions generated by Sturm-Liouville
theory involving spherical harmonics are commonly known as Mehler-Fock
integral transforms. In the inverse transformation formulae, the
subscript of the associated Legendre functions generally appears as the
integration variable while the superscript is either zero or an integer
or a complex number. There is another class of integral transforms
involving associated Legendre functions for which the superscript
appears as the integration variable in the inverse transformation
formulae while the subscript remains fixed. This class of integral
transforms and the associated integral expansions are not widely known
in the literature and they are somewhat related to Mehler-Fock type
transforms. In this book, a number of integral expansions of such type
have been established rigorously and integral expansions of some simple
functions are also obtained as applications. It is hoped that this book
will motivate researchers in applied mathematics to initiate work on
appropriate physical problems in continuum mechanics and
electromagnetic wave diffraction involving conical, toroidal, and
ellipsoidal regions.
Readership: Researchers and graduate students in applied mathematics
and engineering, engineers and physicists working in electromagnetic
diffraction problems and elasticity problems.
Contents:
* Preface
* 1. Introduction
* 2. Integral expansions related to Mehler-Fock transforms
* 3. Integral expansions related to Mehler-Fock type transforms
involving associated Legendre functions
* 4. Integral expansions related to Mehler-Fock type transforms
involving generalized associated Legendre functions
* 5. Some further integral expansions
* Bibliography
Pages: 144
AMS: 44
Subject Classification: Approximation theory, integral transforms and
integral equations, Mechanics of solids, Mathematical physics
Publication Year: 1997
ISBN: 0 582 30816 X

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