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ParabolicCylinderD






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Integration > Definite integration





http://functions.wolfram.com/07.41.21.0014.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) ParabolicCylinderD[\[Nu], t])/E^(a t^2), {t, 0, Infinity}] == ((2^((\[Nu] - \[Alpha])/2) Sqrt[Pi] Gamma[\[Alpha]])/ Gamma[(1 + \[Alpha] - \[Nu])/2]) Hypergeometric2F1[\[Alpha]/2, (\[Alpha] + 1)/2, (1 + \[Alpha] - \[Nu])/2, 1/2 - 2 a] /; (Re[\[Alpha]] > 0 && Re[4 a + 1] > 0) || (0 < Re[\[Alpha]] < -Re[\[Nu]] && Re[4 a + 1] = 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)





2007-05-02





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