Extended Hurwitz results for hypergeometric functions arising in spectral theory

A result of Hurwitz is that the Bessel function J−v(c) (v>0,c>0) has no zeros for 2N<v<2N+1 with integer N. Here corresponding results for hypergeometric and confluent hypergeometric functions are given. Extensions are obtained where the power series are terminated after 2N+1 terms and larger zero-free intervals (2N,V) are found.