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InverseJacobiCD






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiCD[z,m] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/09.37.06.0009.01









  


  










Input Form





InverseJacobiCD[z, m] == InverseJacobiCD[Subscript[z, 0], m] - Sum[(1/k!) Sum[((Pochhammer[1 - k, 2 (k - j) - 2]/((k - j - 1)! (2 Subscript[z, 0])^(k - 2 j - 1))) Sum[Binomial[j, s] Pochhammer[1/2, s] Pochhammer[1/2, j - s] m^(j - s) (1 - Subscript[z, 0]^2)^(-(1/2) - s) (1 - m Subscript[z, 0]^2)^ (s - j - 1/2), {s, 0, j}]) (z - Subscript[z, 0])^k, {j, 0, k - 1}], {k, 1, Infinity}]










Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;1&quot;, &quot;-&quot;, &quot;k&quot;]], &quot;)&quot;]], RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;k&quot;, &quot;-&quot;, &quot;j&quot;]], &quot;)&quot;]]]], &quot;-&quot;, &quot;2&quot;]]], Pochhammer] </annotation> </semantics> <mtext> </mtext> </mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mi> j </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> j </mi> </mrow> <mo> + </mo> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; 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Rule Form





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





2007-05-02