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