- #1
DavideGenoa
- 155
- 5
Hi, friends! I want to show that Hermite functions, defined by ##\varphi_n(x)=(-1)^n e^{x^2/2}\frac{d^n e^{-x^2}}{dx^n}##, ##n\in\mathbb{N}## are an orthogonal system, i.e. that, for any ##m\ne n##,
I have tried by integrating by parts, but I am landing nowhere...
Thank you so much for any help!
##\int_{-\infty}^\infty e^{x^2} \frac{d^m e^{-x^2}}{dx^m} \frac{d^n e^{-x^2}}{dx^n}=0 ##
I have tried by integrating by parts, but I am landing nowhere...
Thank you so much for any help!