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 InverseJacobiNC

 http://functions.wolfram.com/09.43.20.0012.01

 Input Form

 D[InverseJacobiNC[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) ((-8 - 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiNC[z, m], m], m] - (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiNC[z, m], m], m] + (1/(-m + (-1 + m) z^2)^3) (-15 (-1 + m)^3 (-m + (-1 + m) z^2)^3 InverseJacobiNC[z, m] + (1/z) (m ((-z^2 + m (-1 + z^2)) (5 z^4 + 23 m^4 (-1 + z^2)^2 + m^3 (-24 + 83 z^2 - 59 z^4) + m (11 z^2 - 23 z^4) + m^2 (9 - 48 z^2 + 54 z^4)) + (1 - m) Sqrt[1 + m (-1 + 1/z^2)] z (m + z^2 - m z^2)^3 JacobiCD[InverseJacobiNC[z, m], m]) JacobiSD[InverseJacobiNC[z, m], m])))

 Standard Form

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 MathML Form

 3 nc - 1 ( z m ) m 3 1 8 ( m - 1 ) 3 m 3 ( ( - 23 ( m - 1 ) m - 8 ) E ( am ( nc - 1 ( z m ) m ) m ) - ( m - 1 ) ( 11 m - 7 ) F ( am ( nc - 1 ( z m ) m ) m ) + 1 ( ( m - 1 ) z 2 - m ) 3 ( 1 z ( m ( ( 1 - m ) z m ( 1 z 2 - 1 ) + 1 cd ( nc - 1 ( z m ) m ) ( - m z 2 + z 2 + m ) 3 + ( m ( z 2 - 1 ) - z 2 ) ( 23 ( z 2 - 1 ) 2 m 4 + ( - 59 z 4 + 83 z 2 - 24 ) m 3 + ( 54 z 4 - 48 z 2 + 9 ) m 2 + ( 11 z 2 - 23 z 4 ) m + 5 z 4 ) ) sd ( nc - 1 ( z m ) m ) ) - 15 ( m - 1 ) 3 ( ( m - 1 ) z 2 - m ) 3 nc - 1 ( z m ) ) ) m 3 InverseJacobiNC z m 1 8 m -1 3 m 3 -1 -23 m -1 m -8 EllipticE JacobiAmplitude InverseJacobiNC z m m m -1 m -1 11 m -7 EllipticF JacobiAmplitude InverseJacobiNC z m m m 1 m -1 z 2 -1 m 3 -1 1 z -1 m 1 -1 m z m 1 z 2 -1 -1 1 1 2 JacobiCD InverseJacobiNC z m m -1 m z 2 z 2 m 3 m z 2 -1 -1 z 2 23 z 2 -1 2 m 4 -59 z 4 83 z 2 -24 m 3 54 z 4 -1 48 z 2 9 m 2 11 z 2 -1 23 z 4 m 5 z 4 JacobiSD InverseJacobiNC z m m -1 15 m -1 3 m -1 z 2 -1 m 3 InverseJacobiNC z m [/itex]

 Rule Form

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

 2007-05-02