231 Bessel方程的本征值问题 第4页 The figure 23. 1 shows the approximate distribution of the complex zeros of Nn(z) in the region I arg al<T. The figure is symmetrical about the real axis. The two curves on the left extend to infinit having the asymptotes Imz=±-ln3=±0.54931.. There are an infinite number of zeros near each of The two curves extending from z=-n to z=n and bounding an eye-shaped domain intersect the imaginary axis at the points ti(na+b), where Figure 23.1 Zeros of Nn(2) f-1=0.6274 and to=1.19968 is the positive root of cotht=t. There are n zeros near each of these curves. Complex zeros of No(z) Complex zeros of Ni(a) Real part Imaginary part Real part Imaginary part 2.403020.53988 0.78624 5.519880.54718 0.54841 7.01590Wu Chong-shi §23.1 Bessel ➭➯➲➳➵➸➺➻ ➼ 4 ➽ Zeros of Nn(z) The figure 23.1 shows the approximate distribution of the complex zeros of Nn(z) in the region | arg z| ≤ π. The figure is symmetrical about the real axis. The two curves on the left extend to infinity, having the asymptotes Im z = ± 1 2 ln 3 = ±0.54931 . . .. . . There are an infinite number of zeros near each of these curves. The two curves extending from z = −n to z = n and bounding an eye-shaped domain intersect the imaginary axis at the points ±i(na + b), where Figure 23.1 Zeros of Nn(z) a = q t 2 0 − 1 = 0.66274 . . .. . . b = 1 2 q 1 − t −2 0 ln 2 = 0.19146 . . .. . . and t0 = 1.19968 . . .. . . is the positive root of coth t = t. There are n zeros near each of these curves. Complex zeros of N0(z) Complex zeros of N1(z) Real part Imaginary part Real part Imaginary part −2.40302 0.53988 −0.50274 0.78624 −5.51988 0.54718 −3.83353 0.56236 −8.65367 0.54841 −7.01590 0.55339