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.