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WhittakerW






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerW[nu,mu,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/07.45.21.0005.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) WhittakerW[\[Nu], \[Mu], t])/E^(c t), {t, 0, Infinity}] == (-((Pi^2 Csc[2 Pi \[Mu]] Gamma[-\[Alpha] - \[Nu]] (-Tan[Pi (\[Alpha] + \[Mu])] + Tan[Pi (\[Alpha] - \[Mu])]))/ (Gamma[1/2 - \[Alpha] - \[Mu]] Gamma[1/2 - \[Alpha] + \[Mu]] Gamma[1/2 - \[Mu] - \[Nu]] Gamma[1/2 + \[Mu] - \[Nu]]))) Hypergeometric2F1[1/2 + \[Alpha] + \[Mu], 1/2 + \[Alpha] - \[Mu], 1 + \[Alpha] + \[Nu], 1/2 + c] + ((Pi Csc[Pi (\[Alpha] + \[Nu])])/Gamma[1 - \[Alpha] - \[Nu]]) (1/2 + c)^(-\[Alpha] - \[Nu]) Hypergeometric2F1[1/2 + \[Mu] - \[Nu], 1/2 - \[Mu] - \[Nu], 1 - \[Alpha] - \[Nu], 1/2 + c] /; Re[c] > -(1/2) && Re[\[Alpha] + \[Mu]] > -(1/2) && Re[\[Alpha] - \[Mu]] > -(1/2)










Standard Form





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MathML Form







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</ci> <ci> &#956; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <gt /> <apply> <real /> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.