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Dealing with the one-dimensional harmonic oscillator I'm trying to find a general formula for

[tex]

\int_{-\infty}^{\infty} \xi^p H_n(\xi) H_k(\xi) d\xi

[/tex]

there [tex]H_n(\xi) [/tex] and [tex]H_k(\xi)[/tex] are hermite polynomials and p is an integer ( [tex]p\geq 0[/tex]).

I can found the answer for p=0 and p=1 but I can't find the formula for a general p so I need some hint how to do it.

[tex]

\int_{-\infty}^{\infty} \xi^p H_n(\xi) H_k(\xi) d\xi

[/tex]

there [tex]H_n(\xi) [/tex] and [tex]H_k(\xi)[/tex] are hermite polynomials and p is an integer ( [tex]p\geq 0[/tex]).

I can found the answer for p=0 and p=1 but I can't find the formula for a general p so I need some hint how to do it.

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