Legendre Transforms

In+1/2(α), (14.2.7)

where Iν(x) is the modified Bessel function of the first kind.

Example 14.2.2

(a) Tn{(1− x2)−1/2}= π P 2n(0) (14.2.8) (b) Tn

{ 1

2(t− x) } =Qn(t), |t|> 1, (14.2.9)

where Qn(t) is the Legendre function of the second kind given by

Qn(t) = 1 2

(t− x)−1Pn(x)dx.