# T M MacRobert: *Spherical Harmonics* Contents

**Thomas M MacRobert**'s classic text

*Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications*was first published by E P Dutton, London in 1927. The contents of the book are as follows

- 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 Fourier-Bessel expansions.

- Applications of Bessel functions.

A second edition appeared in 1947 published by Methuen, London. It contained the same chapter headings for the first sixteen chapters, but had two additional chapters.

- The hypergeometric function.

- Associated Legendre functions of general order.

In 1967 a third edition of the book was published. Arthur Erdélyi writes that the:-

... 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.

Last Updated August 2007