Non-existence of complex and purely imaginary zeros of a transcendental equation involving Bessel functions (Q1188354)

A specially defined scalar product is employed to deduce a general result on the occurrence of complex zeros of the function \(F(z)J_ a(z)+G(z)J_ a'(z)\) where \(F\) and \(G\) are analytic functions. Included in several corollaries are interesting new results concerning the distribution of zeros of the Bessel function \(J_{ia}'(z)\) of purely imaginary order.