By assuming that the Bessel function defined like as $$ J_\nu(x+y)$$ I want to de-composite it, namely: $$ J_\nu(x+y)=J_\nu(x)*J_\nu(y)$$ or another form. But I don't know how it possible. in fact, I don't want to solve it to reach to answer. Get the final result from a reliable source is enough. I need immediate help.
Asked
Active
Viewed 65 times
0
-
1You may be thinking of DLMF equation 10.23.2 which is an infinite sum. $J_\nu(u+v)=\sum_{k=-\infty}^\infty J_{v+k}(u)J_k(v). $ – Somos Jan 03 '20 at 17:41
-
May be you are right. However, this equation confused me. why the infinite sum? what is its meaning? – Habib Jan 04 '20 at 03:18
-
The generating function DLMF equation 10.12.1 is the ultimate source. – Somos Jan 04 '20 at 03:41