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ParabolicCylinderD






Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Series representations > Asymptotic series expansions





http://functions.wolfram.com/07.41.06.0019.01









  


  










Input Form





ParabolicCylinderD[\[Nu], z] \[Proportional] Piecewise[{{(z^\[Nu] (1 + O[1/z^2]))/E^(z^2/4), Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]}, {(z^\[Nu] (1 + O[1/z^2]))/E^(z^2/4) - ((E^(z^2/4 - I Pi \[Nu]) Sqrt[2 Pi] z^(-1 - \[Nu]))/Gamma[-\[Nu]]) (1 + O[1/z^2]), Arg[z] <= -(Pi/2)}}, (z^\[Nu] (1 + O[1/z^2]))/E^(z^2/4) - ((E^(z^2/4 + I Pi \[Nu]) Sqrt[2 Pi] z^(-1 - \[Nu]))/Gamma[-\[Nu]]) (1 + O[1/z^2])] /; (Abs[z] -> 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)





2007-05-02





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