# §28.9 Zeros

For real each of the functions , , , and has exactly zeros in . They are continuous in . For the zeros of and approach asymptotically the zeros of , and the zeros of and approach asymptotically the zeros of . Here denotes the Hermite polynomial of degree 18.3). Furthermore, for and also have purely imaginary zeros that correspond uniquely to the purely imaginary -zeros of 10.21(i)), and they are asymptotically equal as and . There are no zeros within the strip other than those on the real and imaginary axes.

For further details see McLachlan (1947, pp. 234–239) and Meixner and Schäfke (1954, §§2.331, 2.8, 2.81, and 2.85).