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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/05.01.21.0023.01









  


  










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[2^(n - p) Gamma[1 + n] Gamma[1 + p]])/Gamma[1 + n]) (-\[Zeta])^(-n + p) Hypergeometric1F1Regularized[-n, 1 - n + p, \[Zeta]^2/2])/ 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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