Question

The following polynomial of order n is called Hermite polynomial: 

H"_n − 2ξH'_n + 2n H_n = 0 

Show that: 

(a) H'_n = 2nH_n−1 

(b) H_n+1 = 2ξH_n − 2nH_n−1

Answer 1

Express H_n in terms of a generating function T(ξ,s)