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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/05.01.21.0021.01









  


  










Input Form





Integrate[(HermiteH[n, z]^2 Log[HermiteH[n, z]^2])/E^z^2, {z, -Infinity, Infinity}] == 2^n n! Sqrt[Pi] Log[2^(2 n)] - 2 Sum[Subscript[V, n][Subscript[z, k]], {k, 1, n}] /; HermiteH[n, Subscript[z, k]] == 0 && Subscript[V, n][z] == 2^n n! Sqrt[Pi] (EulerGamma/2 + Log[2] - z^2 HypergeometricPFQ[{1, 1}, {3/2, 2}, -z^2] + (1/2) Sum[(((-1)^k 2^k)/k) Binomial[n, k] Hypergeometric1F1[k, 1/2, -z^2], {k, 1, n}])










Standard Form





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MathML Form







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Rule Form





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2002-12-18





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