A Simple Formula For Calculating Approximate Values of the First Zeros of a Combination Bessel Function Equation (Correspondence)

The solution of many problems in microwave theory, particularly those relating to waveguides having curved boundary surfaces, is dependent upon a determination of the zeros of the Bessel function equation J_p(x) N_p(kx) - J_p(kx) N_p(x) = 0 where J_p and N_p are respectively the Bessel functions of the first and second kinds, of order p. In a majority of the cases arising in waveguide theory, the parameters k and p are real and positive, but may be fractional or integral.