Zeros and Eigenvalues

Abstract

It is evident that for Re(μ) > − 1 the position z = 0 is always one of the zeros of M _{x,μ /2}(z). In what follows this trivial zero will not be considered. We also note once and for all that due to the purely multiplicative branching of M _{x,μ /2}(z) at the origin of the z-plane at each non-vanishing zero, not only the main branch of this function but also any arbitrary branch must vanish. In this respect the behaviour of this function is essentially different from that of the function W _x,μ/2(z).