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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/07.01.21.0008.01









  


  








Input Form





Integrate[(z^(\[Alpha] - 1) HermiteH[\[Nu], z])/E^(p z^2), z] == 2^\[Nu] Sqrt[Pi] ((-(z^\[Alpha]/(2 Gamma[(1 - \[Nu])/2] (p z^2)^(\[Alpha]/2)))) Sum[(Pochhammer[-(\[Nu]/2), k]/(Pochhammer[1/2, k] k! p^k)) Gamma[\[Alpha]/2 + k, p z^2], {k, 0, Infinity}] + (z^(1 + \[Alpha])/(Gamma[-(\[Nu]/2)] (p z^2)^((\[Alpha] + 1)/2))) Sum[(Pochhammer[(1 - \[Nu])/2, k]/(Pochhammer[3/2, k] k! p^k)) Gamma[(\[Alpha] + 1)/2 + k, p z^2], {k, 0, Infinity}])








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