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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==-1





http://functions.wolfram.com/07.11.06.0018.01









  


  










Input Form





LegendreQ[\[Nu], \[Mu], 2, z] == (-(1/(2 Pi))) ((1 - z)^(\[Mu]/2)/(1 + z)^(\[Mu]/2)) (Pi Cos[Pi \[Nu]] Gamma[\[Mu]] (1 - ((\[Nu] (1 + \[Nu]))/(2 (1 - \[Mu]))) (z + 1) - (((1 - \[Nu]) \[Nu] (1 + \[Nu]) (2 + \[Nu]))/ (8 (1 - \[Mu]) (2 - \[Mu]))) (z + 1)^2 + \[Ellipsis]) + (Sin[Pi (\[Mu] - \[Nu])] Cos[Pi (\[Mu] + \[Nu])] Gamma[-\[Mu]] Gamma[\[Mu] - \[Nu]] Gamma[1 + \[Mu] + \[Nu]] (1 + z)^\[Mu] (1 - ((\[Nu] (1 + \[Nu]))/(2 (1 + \[Mu]))) (z + 1) - (((1 - \[Nu]) \[Nu] (1 + \[Nu]) (2 + \[Nu]))/(8 (1 + \[Mu]) (2 + \[Mu]))) (z + 1)^2 + \[Ellipsis]))/(1 - z)^\[Mu]) /; Abs[(z + 1)/2] < 1 && !Element[\[Mu], Integers]










Standard Form





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MathML Form







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</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> &#956; </ci> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </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> <cos /> <apply> <times /> <pi /> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> <ci> &#956; </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; 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</ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.