# §10.42 Zeros

Properties of the zeros of and may be deduced from those of and , respectively, by application of the transformations (10.27.6) and (10.27.8).

For example, if is real, then the zeros of are all complex unless for some positive integer , in which event has two real zeros.

The distribution of the zeros of in the sector in the cases is obtained on rotating Figures 10.21.2, 10.21.4, 10.21.6, respectively, through an angle so that in each case the cut lies along the positive imaginary axis. The zeros in the sector are their conjugates.

has no zeros in the sector ; this result remains true when is replaced by any real number . For the number of zeros of in the sector , when is real, see Watson (1944, pp. 511–513).

For -zeros of , with complex , see Ferreira and Sesma (2008).