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 InverseJacobiSN

 http://functions.wolfram.com/09.48.20.0013.01

 Input Form

 D[InverseJacobiSN[z, m], {m, 3}] == (-(1/(8 (-1 + m)^3 m^3))) ((8 + 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiSN[z, m], m], m] + (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiSN[z, m], m], m] + (1/(1 - m z^2)^(7/2)) (15 (-1 + m)^3 (1 - m z^2)^(7/2) InverseJacobiSN[z, m] + m z ((-1 + m) (-1 + m z^2)^3 JacobiCN[InverseJacobiSN[z, m], m] + Sqrt[1 - m z^2] (-5 + m (12 - 15 m + (11 + 5 m (-6 + 7 m)) z^2 - m (9 + m (-24 + 23 m)) z^4)) (1 - m z^2) JacobiCD[InverseJacobiSN[z, m], m])))

 Standard Form

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 MathML Form

 3 sn - 1 ( z m ) m 3 - 1 8 ( m - 1 ) 3 m 3 ( ( 23 ( m - 1 ) m + 8 ) E ( am ( sn - 1 ( z m ) m ) m ) + ( m - 1 ) ( 11 m - 7 ) F ( am ( sn - 1 ( z m ) m ) m ) + 1 ( 1 - m z 2 ) 7 / 2 ( 15 ( m - 1 ) 3 sn - 1 ( z m ) ( 1 - m z 2 ) 7 / 2 + m z ( ( m - 1 ) cn ( sn - 1 ( z m ) m ) ( m z 2 - 1 ) 3 + 1 - m z 2 ( 1 - m z 2 ) ( m ( - m ( m ( 23 m - 24 ) + 9 ) z 4 + ( 5 m ( 7 m - 6 ) + 11 ) z 2 - 15 m + 12 ) - 5 ) cd ( sn - 1 ( z m ) m ) ) ) ) m 3 InverseJacobiSN z m -1 1 8 m -1 3 m 3 -1 23 m -1 m 8 EllipticE JacobiAmplitude InverseJacobiSN z m m m m -1 11 m -7 EllipticF JacobiAmplitude InverseJacobiSN z m m m 1 1 -1 m z 2 7 2 -1 15 m -1 3 InverseJacobiSN z m 1 -1 m z 2 7 2 m z m -1 JacobiCN InverseJacobiSN z m m m z 2 -1 3 1 -1 m z 2 1 2 1 -1 m z 2 m -1 m m 23 m -24 9 z 4 5 m 7 m -6 11 z 2 -1 15 m 12 -5 JacobiCD InverseJacobiSN 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["InverseJacobiSN", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["8", "+", RowBox[List["23", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", "m"]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["InverseJacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], ",", "m"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", RowBox[List["11", " ", "m"]]]], ")"]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["JacobiAmplitude", "[", RowBox[List[RowBox[List["InverseJacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]], ",", "m"]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["15", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["InverseJacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]]]], "+", RowBox[List["m", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]], ")"]], "3"], " ", RowBox[List["JacobiCN", "[", RowBox[List[RowBox[List["InverseJacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List["12", "-", RowBox[List["15", " ", "m"]], "+", RowBox[List[RowBox[List["(", RowBox[List["11", "+", RowBox[List["5", " ", "m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["7", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["m", " ", RowBox[List["(", RowBox[List["9", "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "24"]], "+", RowBox[List["23", " ", "m"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["z", "4"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["JacobiCD", "[", RowBox[List[RowBox[List["InverseJacobiSN", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]]]]]], ")"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]], ")"]], RowBox[List["7", "/", "2"]]]]]], RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], "3"], " ", SuperscriptBox["m", "3"]]]]]]]]]]

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

 2007-05-02