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 InverseJacobiDS

 http://functions.wolfram.com/09.42.20.0006.01

 Input Form

 D[InverseJacobiDS[z, m], {m, 2}] == (1/(4 (-1 + m)^2 m^2)) ((-2 + 4 m) EllipticE[JacobiAmplitude[InverseJacobiDS[z, m], m], m] + (-1 + m) EllipticF[JacobiAmplitude[InverseJacobiDS[z, m], m], m] + (1/((m + z^2) (-1 + m + z^2)^2)) (3 (m + z^2) (1 + m^2 - z^2 + m (-2 + z^2))^2 InverseJacobiDS[z, m] + m JacobiCS[InverseJacobiDS[z, m], m] (Sqrt[z^2/(m + z^2)] (1 + m^2 - z^2 + m (-2 + z^2)) - (5 m^3 + z^2 - z^4 + m^2 (-7 + 8 z^2) + m (2 - 7 z^2 + 3 z^4)) JacobiDN[InverseJacobiDS[z, m], m])))

 Standard Form

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 MathML Form

 2 ds - 1 ( z m ) m 2 1 4 ( m - 1 ) 2 m 2 ( ( 4 m - 2 ) E ( am ( ds - 1 ( z m ) m ) m ) + ( m - 1 ) F ( am ( ds - 1 ( z m ) m ) m ) + 1 ( z 2 + m ) ( z 2 + m - 1 ) 2 ( 3 ( z 2 + m ) ds - 1 ( z m ) ( m 2 + ( z 2 - 2 ) m - z 2 + 1 ) 2 + m cs ( ds - 1 ( z m ) m ) ( z 2 z 2 + m ( m 2 + ( z 2 - 2 ) m - z 2 + 1 ) - ( - z 4 + z 2 + 5 m 3 + m 2 ( 8 z 2 - 7 ) + m ( 3 z 4 - 7 z 2 + 2 ) ) dn ( ds - 1 ( z m ) m ) ) ) ) m 2 InverseJacobiDS z m 1 4 m -1 2 m 2 -1 4 m -2 EllipticE JacobiAmplitude InverseJacobiDS z m m m m -1 EllipticF JacobiAmplitude InverseJacobiDS z m m m 1 z 2 m z 2 m -1 2 -1 3 z 2 m InverseJacobiDS z m m 2 z 2 -2 m -1 z 2 1 2 m JacobiCS InverseJacobiDS z m m z 2 z 2 m -1 1 2 m 2 z 2 -2 m -1 z 2 1 -1 -1 z 4 z 2 5 m 3 m 2 8 z 2 -7 m 3 z 4 -1 7 z 2 2 JacobiDN InverseJacobiDS z m m [/itex]

 Rule Form

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

 2001-10-29