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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HermiteH[nu,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/07.01.21.0015.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) HermiteH[\[Nu], t])/E^(a t^2), {t, 0, Infinity}] == (2^(-1 + \[Nu]) Sqrt[Pi] ((Gamma[\[Alpha]/2] Hypergeometric2F1[\[Alpha]/2, -(\[Nu]/2), 1/2, 1/a])/ Gamma[(1 - \[Nu])/2] + (Gamma[(1 + \[Alpha])/2]/ (Sqrt[a] \[Alpha] Gamma[1 - \[Nu]/2])) ((-1 + a) Hypergeometric2F1[(1 + \[Alpha])/2, (1 - \[Nu])/2, -(1/2), 1/a] - (-2 + a - \[Alpha] + \[Nu]) Hypergeometric2F1[ (1 + \[Alpha])/2, (1 - \[Nu])/2, 1/2, 1/a])))/a^(\[Alpha]/2) /; Re[a] > 0 && Re[\[Alpha]] > 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)





2001-10-29





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