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 InverseJacobiDN

 http://functions.wolfram.com/09.41.04.0003.01

 Input Form

 InverseJacobiDN[-z, m] == InverseJacobiDN[z, m] - (2/Sqrt[m - 1]) EllipticF[ArcSin[z], 1/(1 - m)]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["InverseJacobiDN", "[", RowBox[List[RowBox[List["-", "z"]], ",", "m"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["InverseJacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "-", RowBox[List[FractionBox["2", SqrtBox[RowBox[List["m", "-", "1"]]]], RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], ",", FractionBox["1", RowBox[List["1", "-", "m"]]]]], "]"]]]]]]]]]]

 MathML Form

 dn - 1 ( - z m ) dn - 1 ( z m ) - 2 m - 1 F ( sin - 1 ( z ) 1 1 - m ) InverseJacobiDN -1 z m InverseJacobiDN z m -1 2 m -1 1 2 -1 EllipticF z 1 1 -1 m -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseJacobiDN", "[", RowBox[List[RowBox[List["-", "z_"]], ",", "m_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["InverseJacobiDN", "[", RowBox[List["z", ",", "m"]], "]"]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", "z", "]"]], ",", FractionBox["1", RowBox[List["1", "-", "m"]]]]], "]"]]]], SqrtBox[RowBox[List["m", "-", "1"]]]]]]]]]]

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

 2001-10-29