Further Formulas for Calculating Approximate Values of the Zeros of Certain Combinations of Bessel Functions (Correspondence)

In a recent letter Gunston has presented a wonderfully simple approximate formula for the smallest z zero of the Bessel function equation J/sub p/(z) N/sub p/ (kz) - J/sub p/(kz)N/sub p/(z) =0(1) where J/sub p/ and N/sub p/ are, respectively, the Bessel functions of the first and second kinds of real-order p. This communication is intended to draw attention to the existence of similar approximate formulas for both the larger z zeros of (1) and the roots of the equally-important companion equationJ'/spl/sub p/(z) N'/sub p/ (kz) - J'/sub p/(kz)N'/sub p/(z) =0 (2) where ' indicates differentiation.