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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Polynomials > HermiteH[n,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/05.01.21.0022.01









  


  










Input Form





Integrate[E^(-(z^2/2) - (1/2) (z - \[Zeta])^2) HermiteH[n, z] HermiteH[p, z - \[Zeta]], {z, -Infinity, Infinity}] == (Sqrt[Pi] Sqrt[2^n n!] Sqrt[2^p p!] Sqrt[(n! p!)/2^(p - n)] (-\[Zeta])^(p - n) Sum[(-(\[Zeta]^2/2))^k/(k! (n - k)! (p - n + k)!), {k, 0, n}])/E^(\[Zeta]^2/4) /; Element[n, Integers] && n >= 0 && Element[p, Integers] && p >= 0










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18





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