Page 72 - Essentials of applied mathematics for scientists and engineers

book Mobk070 March 22, 2007 11:7

62 ESSENTIALS OF APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS

FIGURE 4.2: Bessel functions of the second kind

FIGURE 4.3: The gamma function

Some important relations involving Bessel functions are shown in Table 4.1. We will
derive only the first, namely

d ν ν
(x J ν (x)) = x J ν−1 (x) (4.90)
dx
∞
d ν d (−1) n 2n+2ν
(x J ν (x)) = x (4.91)
dx dx 2 2n+ν n! (n + ν + 1)
n=0