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.