T M MacRobert: Spherical Harmonics Contents

 Fourier series.
 Conduction of heat.
 Transverse vibrations of stretched strings.
 Spherical harmonics; the hypergeometric function.
 The Legendre polynomials.
 The Legendre functions.
 The associated Legendre functions of integral order.
 Applications of Legendre coefficients to potential theory.
 Potentials of spherical shells, spheres, and spheroids.
 Applications to electrostatics.
 Ellipsoids of revolution.
 Eccentric spheres.
 Clerk Maxwell's theory of spherical harmonics.
 Bessel functions.
 Asymptotic expansions and FourierBessel expansions.
 Applications of Bessel functions.

 The hypergeometric function.
 Associated Legendre functions of general order.
... third edition was originally intended as a celebration volume marking the occasion of the author's eightieth birthday in 1964. The author was engaged in a revision of the text when he died in 1962, and the work of revision was completed by I N Sneddon. The revision consists mainly in the addition, in appropriate places, of brief references to newer developments and literature. These will increase the usefulness of the work. 
JOC/EFR August 2007
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