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.

JOC/EFR August 2007
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