Abstract
In the course of an investigation regarding rotating fluids, I have had occasion to make considerable use of Legendre's function of the second kind, which, as is well known, may be expressed in the formwhere Pn is Legendre's polynomial, and fn−1 a polynomial of degree n−1. Various expressions of fn−1 have been given, particularly in terms of Legendre's polynomials of lower degrees; but I found that none was satisfactory in regard to the practical computations which I had to perform.
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