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ParabolicCylinderD






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.41.21.0003.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(z^2/4) ParabolicCylinderD[\[Nu], z], z] == ((2^(\[Nu]/2) Sqrt[Pi] z^\[Alpha])/(\[Alpha] Gamma[(1 - \[Nu])/2])) HypergeometricPFQ[{\[Alpha]/2, -(\[Nu]/2)}, {1/2, \[Alpha]/2 + 1}, z^2/2] - ((2^((\[Nu] + 1)/2) Sqrt[Pi] z^(\[Alpha] + 1))/ ((\[Alpha] + 1) Gamma[-(\[Nu]/2)])) HypergeometricPFQ[ {(\[Alpha] + 1)/2, (1 - \[Nu])/2}, {3/2, (\[Alpha] + 3)/2}, z^2/2]










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)





2007-05-02





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