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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Series representations > Generalized power series > Expansions at z==infinity





http://functions.wolfram.com/07.11.06.0030.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == 2^(-2 - \[Nu]) E^(I Pi \[Mu]) z^(-1 - \[Mu] - \[Nu]) (1 - z^2)^(\[Mu]/2) Sqrt[Pi] Sec[Pi \[Nu]] ((Cos[Pi (\[Mu] + \[Nu])] + E^(I Pi (\[Nu] - \[Mu]))) Gamma[1 + \[Mu] + \[Nu]] Sum[(Pochhammer[(1/2) (1 + \[Mu] + \[Nu]), k] Pochhammer[ (1/2) (2 + \[Mu] + \[Nu]), k])/(Gamma[3/2 + \[Nu] + k] k!)/z^(2 k), {k, 0, Infinity}] + I 2^(1 + 2 \[Nu]) Sin[Pi (\[Mu] - \[Nu])] z^(1 + 2 \[Nu]) Gamma[\[Mu] - \[Nu]] Sum[(Pochhammer[(1/2) (\[Mu] - \[Nu]), k] Pochhammer[ (1/2) (1 + \[Mu] - \[Nu]), k])/(Gamma[1/2 - \[Nu] + k] k!)/z^(2 k), {k, 0, Infinity}]) /; Abs[z] > 1










Standard Form





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MathML Form







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</ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <imaginaryi /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <plus /> <ci> &#956; 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</ci> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <times /> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -2 </cn> <ci> k </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> k </ci> <ci> &#957; 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Rule Form





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





2001-10-29





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