When a function has been expressed as a series of spherical harmonics with constant coefficients, the determination of these coefficients from given values of the function is in the general case one of the most complicated operations which can be set before the calculator.

Since Gauss first carried out these operations in a calculation of this kind, efforts have not been wanting to simplify them and make their frequent application possible. The most successful of all in this respect was Franz Neumann, who showed that by a suitable choice of the argument the calculation could be materially shortened.