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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.10.06.0016.01









  


  








Input Form





LegendreQ[\[Nu], z] == (2^(-\[Nu] - 2)/Sqrt[Pi]) (z - 1)^(-\[Nu] - 1) (((2^(2 \[Nu] + 1) Gamma[1/2 + \[Nu]])/Gamma[1 + \[Nu]]) (z - 1)^(2 \[Nu] + 1) (Log[1 + z] - Log[-z - 1]) (1 - \[Nu]/(1 - z) - ((1 - \[Nu])^2 \[Nu])/((1 - 2 \[Nu]) (1 - z)^2) + \[Ellipsis]) + (Gamma[-(1/2) - \[Nu]]/Gamma[-\[Nu]]) (2 Pi Cot[Pi \[Nu]] + Log[1 + z] - Log[-z - 1]) (1 + (1 + \[Nu])/(1 - z) + ((1 + \[Nu]) (2 + \[Nu])^2)/ ((3 + 2 \[Nu]) (1 - z)^2) + \[Ellipsis])) /; Abs[1 - z] > 2 && !Element[\[Nu], Integers]








Standard Form





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MathML Form







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</mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LegendreQ </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; 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Rule Form





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





2001-10-29