Question

Bessel functions recurrence relation their derivatives relation

Answer 1

Calculate the Derive-ative of G(x,h) on the LHS and your Bessel sum on the RHS!

ddxexp{x2(h−1h)}=12(h−1h)∑−∞∞hnJn(x)=12(∑−∞∞hnJn−1(x)−∑−∞∞hnJn+1(x))ddx∑−∞∞hnJn(x)=∑−∞∞hnddxJn(x)
Now compare entries with equal hn...