Riccati equations and convolution formulae for functions of Rayleigh type

Kishore (1963 Proc Am. Math. Soc. 14 527) considered the Rayleigh functions sigma(n)(nu) = Sigma(k=1)(infinity) j(nu k)(-2n), n = 1, 2,..., where +/-j (nu k) are the (non-zero) zeros of the Bessel function J(nu)(z) and provide d 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 funct ions. Here we extend this result to a larger class of functions by using Ri ccati differential equations. We get new results for the zeros of certain c ombinations of Bessel functions and their first and second derivatives as w ell as recovering some results of Buchholz for zeros of confluent hypergeom etric functions.