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ParabolicCylinderD




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ParabolicCylinderD[nu,z] > Integral transforms > Laplace transforms





http://functions.wolfram.com/07.41.22.0001.01









  


  








Input Form





LaplaceTransform[t^(\[Alpha] - 1) ParabolicCylinderD[\[Nu], Sqrt[t]], t, z] == ((2^(\[Nu]/2 - \[Alpha] + 1) Sqrt[Pi] Gamma[2 \[Alpha]])/ Gamma[(1 - \[Nu])/2 + \[Alpha]]) Hypergeometric2F1[\[Alpha], \[Alpha] + 1/2, (1 - \[Nu])/2 + \[Alpha], 1/2 - 2 z] /; (Re[\[Alpha]] > 0 && Re[4 z + 1] > 0) || (0 < Re[\[Alpha]] < -(Re[\[Nu]]/2) && Re[4 z + 1] = 0)








Standard Form





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MathML Form







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</ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <real /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <ci> Set </ci> <apply> <and /> <apply> <lt /> <cn type='integer'> 0 </cn> <apply> <real /> <ci> &#945; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <real /> <ci> &#957; </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <real /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02