Zeros of combinations of bessel functions and their derivatives

We use the Mittag-Leffler partial fractions expansion of and certain monotonicity properties of this and related functions to study the zeros of where α, β, τ and δ are real. Thus we simplify and, in roost cases, strengthen results of E. K Ifantis and P. D. Siafarikas, Applicable Anal. 23 (1986), 85-110. We derive further properties of these zeros in certain special cases