N Kishore (1963 Proc. Am. Math. Soc. 14 527) considered the Rayleigh functions , , where the are the (non-zero) zeros of the Bessel function and provided a convolution-type sum formula for finding in terms of . Here we investigate corresponding expressions for sums of reciprocal powers of zeros of derivatives and other functions related to Bessel functions. It turns out that we can get results similar to Kishore's expressing in terms of and .