- #1
mathmajor314
- 9
- 0
I am not sure how to format in LaTeX; I apologize for that.
The Hermite polynomials Hn(x) (physicist's version) satisfy
the recurrence relation,
H_{n+1}(x) - 2xHn(x) + 2nH_{n-1}(x) = 0; H0(x) = 1 and H1(x) = 2x:
Use this to derive the generating function for the Hermite polynomials, exp(2tx-t^2).
So far, I have gotten to Sum(H_{n+1}*exp(t)) = Sum{H_{n}[2x*exp(t)-2t*exp(t)]}.
I know I need to then integrate this then use H0(x) = 1 and H1(x) = 2x to solve for the constant of integration but I'm not sure how to do that.
The Hermite polynomials Hn(x) (physicist's version) satisfy
the recurrence relation,
H_{n+1}(x) - 2xHn(x) + 2nH_{n-1}(x) = 0; H0(x) = 1 and H1(x) = 2x:
Use this to derive the generating function for the Hermite polynomials, exp(2tx-t^2).
So far, I have gotten to Sum(H_{n+1}*exp(t)) = Sum{H_{n}[2x*exp(t)-2t*exp(t)]}.
I know I need to then integrate this then use H0(x) = 1 and H1(x) = 2x to solve for the constant of integration but I'm not sure how to do that.