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 InverseJacobiSD

 http://functions.wolfram.com/09.47.20.0012.01

 Input Form

 D[InverseJacobiSD[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiSD[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiSD[z, m], m], m] + (-15 (-1 + m + (-1 + m)^2 z^2)^3 (1 + m z^2)^2 InverseJacobiSD[z, m] + m JacobiCN[InverseJacobiSD[z, m], m] ((-(-1 + m)) m z (6 + 2 (-9 + 19 m) z^2 + (13 - 69 m + 78 m^2) z^4 + (-1 + m (23 - 80 m + 66 m^2)) z^6 + (-1 + m) m (-2 + m (-9 + 20 m)) z^8) + (1 + m z^2) ((-(-1 + m)) (1 + (-1 + m) z^2) Sqrt[1/(1 + m z^2)] (-1 + (-3 + 5 m) z^2 + (4 + m (-18 + 17 m)) z^4 + (-1 + m) m (-7 + 11 m) z^6) + (5 - 18 m + 21 m^2 + 2 (-5 + m (32 + m (-73 + 54 m))) z^2 + (5 + m (-58 + m (231 - 376 m + 206 m^2))) z^4 + 2 (-1 + m) m (-6 + m (43 + m (-109 + 86 m))) z^6 + (-1 + m)^2 m^2 (7 + m (-36 + 53 m)) z^8) JacobiDN[InverseJacobiSD[z, m], m]) JacobiSN[InverseJacobiSD[z, m], m]))/((1 + (-1 + m) z^2)^3 (1 + m z^2)^2))

 Standard Form

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RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["InverseJacobiSD", "[", RowBox[List["z", ",", "m"]], "]"]], ",", "m"]], "]"]]]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]], " ", SuperscriptBox["z", "2"]]]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["m", " ", SuperscriptBox["z", "2"]]]]], ")"]], "2"]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 3 sd - 1 ( z m ) m 3 1 8 ( m - 1 ) 3 m 3 ( ( - 23 ( m - 1 ) m - 8 ) E ( am ( sd - 1 ( z m ) m ) m ) - ( m - 1 ) ( 11 m - 7 ) F ( am ( sd - 1 ( z m ) m ) m ) + 1 ( ( m - 1 ) z 2 + 1 ) 3 ( m z 2 + 1 ) 2 ( m cn ( sd - 1 ( z m ) m ) ( ( m z 2 + 1 ) ( ( ( m - 1 ) 2 m 2 ( m ( 53 m - 36 ) + 7 ) z 8 + 2 ( m - 1 ) m ( m ( m ( 86 m - 109 ) + 43 ) - 6 ) z 6 + ( m ( m ( 206 m 2 - 376 m + 231 ) - 58 ) + 5 ) z 4 + 2 ( m ( m ( 54 m - 73 ) + 32 ) - 5 ) z 2 + 21 m 2 - 18 m + 5 ) dn ( sd - 1 ( z m ) m ) - ( m - 1 ) ( ( m - 1 ) z 2 + 1 ) 1 m z 2 + 1 ( ( m - 1 ) m ( 11 m - 7 ) z 6 + ( m ( 17 m - 18 ) + 4 ) z 4 + ( 5 m - 3 ) z 2 - 1 ) ) sn ( sd - 1 ( z m ) m ) - ( m - 1 ) m z ( ( m - 1 ) m ( m ( 20 m - 9 ) - 2 ) z 8 + ( m ( 66 m 2 - 80 m + 23 ) - 1 ) z 6 + ( 78 m 2 - 69 m + 13 ) z 4 + 2 ( 19 m - 9 ) z 2 + 6 ) ) - 15 ( ( m - 1 ) 2 z 2 + m - 1 ) 3 ( m z 2 + 1 ) 2 sd - 1 ( z m ) ) ) m 3 InverseJacobiSD z m 1 8 m -1 3 m 3 -1 -23 m -1 m -8 EllipticE JacobiAmplitude InverseJacobiSD z m m m -1 m -1 11 m -7 EllipticF JacobiAmplitude InverseJacobiSD z m m m 1 m -1 z 2 1 3 m z 2 1 2 -1 m JacobiCN InverseJacobiSD z m m m z 2 1 m -1 2 m 2 m 53 m -36 7 z 8 2 m -1 m m m 86 m -109 43 -6 z 6 m m 206 m 2 -1 376 m 231 -58 5 z 4 2 m m 54 m -73 32 -5 z 2 21 m 2 -1 18 m 5 JacobiDN InverseJacobiSD z m m -1 m -1 m -1 z 2 1 1 m z 2 1 -1 1 2 m -1 m 11 m -7 z 6 m 17 m -18 4 z 4 5 m -3 z 2 -1 JacobiSN InverseJacobiSD z m m -1 m -1 m z m -1 m m 20 m -9 -2 z 8 m 66 m 2 -1 80 m 23 -1 z 6 78 m 2 -1 69 m 13 z 4 2 19 m -9 z 2 6 -1 15 m -1 2 z 2 m -1 3 m z 2 1 2 InverseJacobiSD z m [/itex]

 Rule Form

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

 2007-05-02