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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,2,z] > Representations through more general functions > Through Meijer G > Generalized cases involving sgn





http://functions.wolfram.com/07.11.26.0025.01









  


  










Input Form





((Sign[Abs[z] - 1] (z^2 - 1))^(1/2 + \[Nu])/Sqrt[1 + z]) LegendreQ[\[Nu], 1/2 + \[Nu], 2, (2 Sqrt[z])/(1 + z)] == (-((2^(-(5/2) - \[Nu]) Tan[Pi \[Nu]])/(Gamma[-(1/2) - 2 \[Nu]] Gamma[-\[Nu]]))) MeijerG[{{1 + \[Nu], 5/4 + \[Nu]}, {}}, {{0, 1/4}, {}}, z, 1/2] + 2^(-(3/2) - \[Nu]) Gamma[1 + \[Nu]] Gamma[3/2 + 2 \[Nu]] Sec[Pi \[Nu]] (Sin[Pi (\[Nu] + 1/4)] MeijerG[{{\[Nu] + 5/4}, {\[Nu] + 1}}, {{0}, {1/4}}, z, 1/2] + Cos[Pi (\[Nu] + 1/4)] MeijerG[{{\[Nu] + 1}, {\[Nu] + 5/4}}, {{1/4}, {0}}, z, 1/2]) /; Re[z] > 0










Standard Form





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MathML Form







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</mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 5 </mn> <mn> 4 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;2&quot;]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;2&quot;], MeijerG, Rule[Editable, True]]]], MeijerG], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;\[Nu]&quot;, &quot;+&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;\[Nu]&quot;, &quot;+&quot;, FractionBox[&quot;5&quot;, &quot;4&quot;]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox[&quot;1&quot;, &quot;4&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mrow> <mi> sin </mi> <mo> &#8290; 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</ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <ci> &#915; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 5 <sep /> 4 </cn> </apply> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </list> <list /> </list> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <times /> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </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.