I need to evaluate the following integral:
I need the result to construct the first 5 Hermite polynomials.
The Attempt at a Solution
First I tried arbitrary values for "m" and "n". I was not able to evaluate the integral when (m+n) was even. I found that when (m+n) is odd, the integral is equal to 0. This makes sense since e^(-x^2) is an even function.
Then I looked it up. Using wolfram integral calculator left me with something known as the incomplete gamma function (Not very sure what that is) in the solution. Maple gave me a very long answer that involved something labeled as Whittaker M.
Finally I went to my professor to ask him how to evaluate it. He said that it is an integral that can be looked up and I should have a square root pi in my answer. He also said that the incomplete gamma function should not be there.
I am not too sure of how to evaluate the integral myself. Maybe more importantly, I am not sure where to find the result of the integral if it can indeed be "looked up". Thanks for reading.