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variants of this functions
LegendreP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreP[nu,mu,3,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.09.20.0015.01









  


  








Input Form





D[LegendreP[\[Nu], \[Mu], 3, z], {z, m}] == Sqrt[Pi] Sum[((-1)^(m - k) (z - 1)^((k - m)/2) (z + 1)^((k - m)/2) Binomial[m, k] Pochhammer[-\[Mu] - \[Nu], m - k] HypergeometricPFQRegularized[{1, -k, \[Mu]/2}, {(1 - k)/2, 1 - k/2}, z^2/(z^2 - 1)] Pochhammer[1 - \[Mu] + \[Nu], m - k] LegendreP[\[Nu], k - m + \[Mu], 3, z])/z^k, {k, 0, m}] /; Element[m, Integers] && m >= 0








Standard Form





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MathML Form







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</mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#956; </mi> <mo> + </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mi> k </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;\[Mu]&quot;, &quot;+&quot;, &quot;\[Nu]&quot;]], &quot;)&quot;]], RowBox[List[&quot;m&quot;, &quot;-&quot;, &quot;k&quot;]]], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <msubsup> <semantics> <mi> &#120083; </mi> <annotation encoding='Mathematica'> TagBox[TagBox[TagBox[&quot;\[GothicCapitalP]&quot;, LegendreQ], LegendreQ], LegendreP] </annotation> </semantics> <mi> &#957; </mi> <mrow> <mi> k </mi> <mo> - </mo> <mi> m </mi> <mo> + </mo> <mi> &#956; </mi> </mrow> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, HoldComplete[LegendreP, 3]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; 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</ci> </apply> <ci> &#957; </ci> </apply> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreP </ci> <apply> <ci> LegendreQ </ci> <apply> <ci> LegendreQ </ci> <ci> &#120083; </ci> </apply> </apply> </apply> <ci> &#957; </ci> </apply> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <ci> &#956; </ci> </apply> </apply> <apply> <apply> <ci> HoldComplete </ci> <ci> LegendreP </ci> <cn type='integer'> 3 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02