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InverseJacobiCD




Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiCD[z,m] > Series representations > Generalized power series > Expansions at m==0





http://functions.wolfram.com/09.37.06.0004.01









  


  








Input Form





InverseJacobiCD[z, m] == Sum[((Pi Pochhammer[1/2, k] Pochhammer[1/2, k])/(2 k!^2) - ((Pochhammer[1/2, k] z^(2 k + 1))/((1 + 2 k) k!)) Hypergeometric2F1[1/2, 1/2 + k, 3/2 + k, z^2]) m^k, {k, 0, Infinity}]








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> cd </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;], &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;], &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mi> k </mi> <mo> ! 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiCD", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]]]], RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["k", "!"]], ")"]], "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "+", "k"]], ",", RowBox[List[FractionBox["3", "2"], "+", "k"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], " ", RowBox[List["k", "!"]]]]]]], ")"]], " ", SuperscriptBox["m", "k"]]]]]]]]]


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





2001-10-29