Confluent Hypergeometric Function

1. Jun 21, 2012

M. next

1. The problem statement, all variables and given/known data
Hermite differential equation: y"(x) -2xy'(x)+2ny(x)=0

2. Relevant equations: y(x)=C$_{n}$(x)H$_{n}$(x) though it wont have to do with my 1st question directly & change of variable: z=x$^{2}$

3. The attempt at a solution: procedure: dy/dx=2$\sqrt{z}$dy/dz
1st Question: I want to find now the second derivative: d$^{2}$y/dx$^{2}$ ... But all my attempts turn out to fail.

2nd Question: Also why did we say y(x)=C$_{n}$(x)H$_{n}$(x)