Published online by Cambridge University Press: 24 October 2008
Williams ((3)) has transformed certain series equations in Legendre functions to Bessel integral equations; his main result being that if
then
and vice versa. (Here, n is written for Williams's n + m. The coefficients an are related to Williams's An by a factor. There is an extra factor 2 in equation (7) in Williams's paper which appears to be an error.)