  N. Kishore, Proc. Amer. Math. Soc. 14 (1963), 523, considered the Rayleigh
functions sigma_n, sums of the negative even powers of the (non-zero) zeros of
the Bessel function J_nu(z) and provided a convolution type sum formula for
finding sigma_n in terms of sigma_1, ...,sigma_{n-1}. His main tool was the
recurrence relation for Bessel functions. Here we extend this result to a
larger class of functions by using Riccati ifferential equations. We get new
results for the zeros of certain combinations of Bessel functions and their
first and second derivatives as well as recovering some results of Buchholz for
zeros of confluent hypergeometric functions.
