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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/07.11.06.0034.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] \[Proportional] ((2^(-2 - \[Nu]) Sqrt[Pi] Csc[Pi \[Mu]])/Gamma[-\[Mu] - \[Nu]]) z^(-\[Nu] - 1) ((1 - z)^(\[Mu]/2)/(1 + z)^(\[Mu]/2)) (Gamma[-(1/2) - \[Nu]] (Cos[Pi \[Mu]] ((1 + z)^\[Mu]/(1 - z)^\[Mu]) + Csc[Pi (\[Mu] + \[Nu])] Sin[Pi (\[Mu] - \[Nu])]) (1 + O[1/z]) - ((2^(2 \[Nu] + 1) Gamma[1/2 + \[Nu]] Gamma[-\[Mu] - \[Nu]])/ Gamma[1 - \[Mu] + \[Nu]]) z^(2 \[Nu] + 1) (1 - Cos[Pi \[Mu]] ((1 + z)^\[Mu]/(1 - z)^\[Mu])) (1 + O[1/z])) /; (Abs[z] -> Infinity) && !Element[\[Mu], Integers]










Standard Form





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MathML Form







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</annotation> </semantics> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#956; </mi> <mo> &#8713; </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> <ci> Proportional </ci> <apply> <ci> LegendreQ </ci> <ci> &#957; </ci> <ci> &#956; </ci> <cn type='integer'> 2 </cn> <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 /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <csc /> <apply> <times /> <pi /> <ci> &#956; </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; 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Rule Form





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





2001-10-29