Bessel function around two points

Question

Hi does any know how to calculate Bessel function for point module 2.

I have two point $x_1=2 i^{1/2}$ and $x_2=2 i^{3/2}$

I need to check if they satisfy P=0 where

$P= c_1 J_{s} (x_1) + c_2 J_{s}(x_2)$ with c costants or to calculate any way P

Answer 1

I think I solved with the definition of J as series.

$J_s(x) = \sum_{k=0}^{\infty}(-1)^m (x/2)^{2m+s}/m! \Gamma(m+s+1)$

The result indeed with this zero for apposite costant.