Chapter 11.6, Problem 1P

Problems

Use the relations $\left(\mathrm{11.6.4}\right)$ and $\left(\mathrm{11.6.5}\right)$ to show that if $p$ is a half integer, then Bessel’s equation of order $p$ has two linearly independent Forbenius series solutions.

$\left[{\left(r+1\right)}^2-p^2\right]a_1=0$ … $\left(\mathrm{11.6.4}\right)$

$\left[{\left(r+n\right)}^2-p^2\right]a_n=-a_{n-2},n=2,3\dots$ ... $\left(\mathrm{11.6.5}\right)$