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##,(adsbygoogle = window.adsbygoogle || []).push({});

##\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!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Orthogonality of Hermite functions

Loading...

Similar Threads for Orthogonality Hermite functions |
---|

I Approximating different functions |

I Equality between functions |

I Deriving a function from within an integral with a known solution |

I Integrate a function over a closed circle-like contour around an arbitrary point on a torus |

B Function rules question |

**Physics Forums | Science Articles, Homework Help, Discussion**