Calculating Integrals with Hermite Polynomials

Thread starter alejandrito29
Start date Sep 7, 2013
Tags

Hermite polynomials Polynomials

Sep 7, 2013

alejandrito29

Hello , i need to calculate the following integral

\int_{-\infty}^{\infty} x^4 H(x)^2 e^{-x^2} dx

i tried using the recurrence relation, but i don't go the answer

Physics news on Phys.org

Scientist returns to microbial roots and discovers potential quantum computing advancement
Physicists achieve record precision in measuring proton-to-electron mass ratio with H₂⁺
Quantum calculations provide a sharper image of subatomic stress

Sep 7, 2013

vanhees71

Science Advisor

Education Advisor

Insights Author

What's H? The Hermite polynomials have an index, i.e., H_n with n \in \mathbb{N}_0.

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

View full post »

Thread 'Solve this problem that involves induction'

Hello, This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread. Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).

View full post »