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InverseJacobiSD






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.47.06.0004.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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










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





2001-10-29