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 JacobiZeta

 http://functions.wolfram.com/08.07.06.0021.01

 Input Form

 JacobiZeta[z, m] \[Proportional] (1 - EllipticE[m]/EllipticK[m]) z (1 + O[z^2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["JacobiZeta", "[", RowBox[List["z", ",", "m"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["EllipticE", "[", "m", "]"]], RowBox[List["EllipticK", "[", "m", "]"]]]]], ")"]], "z", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", SuperscriptBox["z", "2"], "]"]]]], ")"]]]]]]]]

 MathML Form

 Ζ ( z m ) ( 1 - E ( m ) K ( m ) ) z ( 1 + O ( z 2 ) ) Proportional JacobiZeta z m 1 -1 EllipticE m EllipticK m -1 z 1 O z 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiZeta", "[", RowBox[List["z_", ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["EllipticE", "[", "m", "]"]], RowBox[List["EllipticK", "[", "m", "]"]]]]], ")"]], " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox[RowBox[List["O", "[", "z", "]"]], "2"]]], ")"]]]]]]]]

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

 2007-05-02