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 JacobiSN

 http://functions.wolfram.com/09.36.16.0172.01

 Input Form

 JacobiSN[z - EllipticK[m] - I EllipticK[1 - m], m] == (-(1/Sqrt[m])) JacobiDC[z, m]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["z", "-", RowBox[List["EllipticK", "[", "m", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m"]], "]"]]]]]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", SqrtBox["m"]]]], " ", RowBox[List["JacobiDC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]]

 MathML Form

 sn ( z - K ( 1 - m ) - K ( m ) m ) - dc ( z m ) m JacobiSN z -1 EllipticK 1 -1 m -1 EllipticK m m -1 JacobiDC z m m 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["z_", "-", RowBox[List["EllipticK", "[", "m_", "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["EllipticK", "[", RowBox[List["1", "-", "m_"]], "]"]]]]]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["JacobiDC", "[", RowBox[List["z", ",", "m"]], "]"]], SqrtBox["m"]]]]]]]]

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

 2007-05-02

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