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ParabolicCylinderD




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.41.06.0016.01









  


  








Input Form





ParabolicCylinderD[\[Nu], z] \[Proportional] (-(((z^2)^(-1 - \[Nu]/2) Sin[Pi \[Nu]])/Sqrt[2 Pi])) (E^(z^2/4) (-z + Sqrt[z^2]) Gamma[1 + \[Nu]] HypergeometricPFQ[ {(1 + \[Nu])/2, (2 + \[Nu])/2}, {}, 2/z^2] + (Sqrt[Pi/2] Sqrt[-z^2] (-z^4)^(\[Nu]/2) (Sqrt[-z^2] Csc[(Pi \[Nu])/2] + z Sec[(Pi \[Nu])/2]) HypergeometricPFQ[{-(\[Nu]/2), (1 - \[Nu])/2}, {}, -(2/z^2)])/E^(z^2/4)) /; (Abs[z] -> Infinity)








Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <csc /> <apply> <times /> <pi /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <sec /> <apply> <times /> <pi /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02