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 InverseJacobiCS

 http://functions.wolfram.com/09.39.20.0012.01

 Input Form

 D[InverseJacobiCS[z, m], {m, 3}] == (-(1/(4 (-1 + m)^3 m^3 (1 - m + z^2)^2))) ((1/2) (-1 + m - z^2) ((8 + 23 (-1 + m) m) (-1 + m - z^2) EllipticE[JacobiAmplitude[InverseJacobiCS[z, m], m], m] + (-1 + m) (m z Sqrt[1 - m/(1 + z^2)] + (-7 + 11 m) (-1 + m - z^2) EllipticF[JacobiAmplitude[InverseJacobiCS[z, m], m], m])) + (1/(2 (1 + z^2))) (15 (-1 + m)^3 (1 + z^2) (1 - m + z^2)^2 InverseJacobiCS[z, m] - m z ((-1 + m)^2 (5 + m (-13 + 23 m)) - 5 (-1 + m) (2 + m (-5 + 7 m)) z^2 + (5 + 3 m (-4 + 5 m)) z^4) JacobiND[InverseJacobiCS[z, m], m]))

 Standard Form

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 MathML Form

 3 cs - 1 ( z m ) m 3 - 1 4 ( m - 1 ) 3 m 3 ( z 2 - m + 1 ) 2 ( 1 2 ( - z 2 + m - 1 ) ( ( 23 ( m - 1 ) m + 8 ) ( - z 2 + m - 1 ) E ( am ( cs - 1 ( z m ) m ) m ) + ( m - 1 ) ( m 1 - m z 2 + 1 z + ( 11 m - 7 ) ( - z 2 + m - 1 ) F ( am ( cs - 1 ( z m ) m ) m ) ) ) + 1 2 ( z 2 + 1 ) ( 15 ( m - 1 ) 3 ( z 2 + 1 ) ( z 2 - m + 1 ) 2 cs - 1 ( z m ) - m z ( ( 3 m ( 5 m - 4 ) + 5 ) z 4 - 5 ( m - 1 ) ( m ( 7 m - 5 ) + 2 ) z 2 + ( m - 1 ) 2 ( m ( 23 m - 13 ) + 5 ) ) nd ( cs - 1 ( z m ) m ) ) ) m 3 InverseJacobiCS z m -1 1 4 m -1 3 m 3 z 2 -1 m 1 2 -1 1 2 -1 z 2 m -1 23 m -1 m 8 -1 z 2 m -1 EllipticE JacobiAmplitude InverseJacobiCS z m m m m -1 m 1 -1 m z 2 1 -1 1 2 z 11 m -7 -1 z 2 m -1 EllipticF JacobiAmplitude InverseJacobiCS z m m m 1 2 z 2 1 -1 15 m -1 3 z 2 1 z 2 -1 m 1 2 InverseJacobiCS z m -1 m z 3 m 5 m -4 5 z 4 -1 5 m -1 m 7 m -5 2 z 2 m -1 2 m 23 m -13 5 JacobiND InverseJacobiCS z m m [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["m_", ",", "3"]], "}"]]]]], RowBox[List["InverseJacobiCS", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m", "-", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["8", "+", RowBox[List["23", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", "m"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m", "-", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], ",", "m"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["m", " ", "z", " ", SqrtBox[RowBox[List["1", "-", FractionBox["m", RowBox[List["1", "+", SuperscriptBox["z", "2"]]]]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", RowBox[List["11", " ", "m"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m", "-", SuperscriptBox["z", "2"]]], ")"]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], ",", "m"]], "]"]]]]]], ")"]]]]]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List["15", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], "3"], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "m", "+", SuperscriptBox["z", "2"]]], ")"]], "2"], " ", RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]]]], "-", RowBox[List["m", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "13"]], "+", RowBox[List["23", " ", "m"]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["7", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["5", "+", RowBox[List["3", " ", "m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["5", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["JacobiND", "[", RowBox[List[RowBox[List["InverseJacobiCS", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]]]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]]]]]]], RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], "3"], " ", SuperscriptBox["m", "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "m", "+", SuperscriptBox["z", "2"]]], ")"]], "2"]]]]]]]]]]

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

 2007-05-02