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 InverseJacobiCN

 http://functions.wolfram.com/09.38.20.0013.01

 Input Form

 D[InverseJacobiCN[z, m], {m, 3}] == (-(1/(8 (-1 + m)^3 m^3))) ((8 + 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiCN[z, m], m], m] + (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[ InverseJacobiCN[z, m], m], m] + 15 (-1 + m)^3 InverseJacobiCN[z, m] - (1/(1 + m (-1 + z^2))^(7/2)) ((-m) (-1 + z^2) z ((-1 + m) (1 + m (-1 + z^2))^3 JacobiNS[InverseJacobiCN[z, m], m] + ((-1 + m)^2 (5 + m (-13 + 23 m)) - (-1 + m) m (11 + m (-37 + 46 m)) z^2 + m^2 (9 + m (-24 + 23 m)) z^4) Sqrt[1 + m (-1 + z^2)] JacobiDS[InverseJacobiCN[z, m], m])))

 Standard Form

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 MathML Form

 3 cn - 1 ( z m ) m 3 - 1 8 ( m - 1 ) 3 m 3 ( 15 cn - 1 ( z m ) ( m - 1 ) 3 + ( 11 m - 7 ) F ( am ( cn - 1 ( z m ) m ) m ) ( m - 1 ) + ( 23 ( m - 1 ) m + 8 ) E ( am ( cn - 1 ( z m ) m ) m ) - - 1 ( m ( z 2 - 1 ) + 1 ) 7 / 2 ( m ( z 2 - 1 ) z ( ( m - 1 ) ns ( cn - 1 ( z m ) m ) ( m ( z 2 - 1 ) + 1 ) 3 + ( m 2 ( m ( 23 m - 24 ) + 9 ) z 4 - ( m - 1 ) m ( m ( 46 m - 37 ) + 11 ) z 2 + ( m - 1 ) 2 ( m ( 23 m - 13 ) + 5 ) ) ds ( cn - 1 ( z m ) m ) m ( z 2 - 1 ) + 1 ) ) ) m 3 InverseJacobiCN z m -1 1 8 m -1 3 m 3 -1 15 InverseJacobiCN z m m -1 3 11 m -7 EllipticF JacobiAmplitude InverseJacobiCN z m m m m -1 23 m -1 m 8 EllipticE JacobiAmplitude InverseJacobiCN z m m m -1 -1 1 m z 2 -1 1 7 2 -1 m z 2 -1 z m -1 JacobiNS InverseJacobiCN z m m m z 2 -1 1 3 m 2 m 23 m -24 9 z 4 -1 m -1 m m 46 m -37 11 z 2 m -1 2 m 23 m -13 5 JacobiDS InverseJacobiCN z m m m z 2 -1 1 1 2 [/itex]

 Rule Form

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

 2007-05-02