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variants of this functions
HermiteH






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HermiteH[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function





http://functions.wolfram.com/07.01.21.0009.01









  


  










Input Form





Integrate[(z^(\[Alpha] - 1) HermiteH[\[Nu], a z])/E^(a^2 z^2), z] == 2^(-1 + \[Nu]) Pi z^\[Alpha] ((1/Gamma[(1 - \[Nu])/2]) (Gamma[\[Alpha]/2] HypergeometricPFQRegularized[ {(1 + \[Nu])/2, \[Alpha]/2}, {1/2, (2 + \[Alpha])/2}, (-a^2) z^2]) - (1/Gamma[-(\[Nu]/2)]) (a z Gamma[(1 + \[Alpha])/2] HypergeometricPFQRegularized[{(2 + \[Nu])/2, (1 + \[Alpha])/2}, {3/2, (3 + \[Alpha])/2}, (-a^2) z^2]))










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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