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 InverseJacobiDS

 http://functions.wolfram.com/09.42.20.0012.01

 Input Form

 D[InverseJacobiDS[z, m], {m, 3}] == (1/(8 (-1 + m)^3 m^3)) (-15 (-1 + m)^3 InverseJacobiDS[z, m] + ((-z) (-1 + m + z^2)^3 (m + z^2) ((8 + 23 (-1 + m) m) EllipticE[JacobiAmplitude[InverseJacobiDS[z, m], m], m] + (-1 + m) (-7 + 11 m) EllipticF[JacobiAmplitude[InverseJacobiDS[z, m], m], m]) + m z JacobiCN[InverseJacobiDS[z, m], m] ((-(-1 + m)) m z ((-1 + m) m (-2 + 5 m) + (1 + m (-7 + 8 m)) z^2 + (-1 + 3 m) z^4) - (-1 + m) (-1 + m + z^2) Sqrt[z^2/(m + z^2)] ((-1 + m) m (-7 + 12 m) + (4 + m (-19 + 18 m)) z^2 + (-3 + 5 m) z^4 - z^6) JacobiSN[InverseJacobiDS[z, m], m] + JacobiDN[InverseJacobiDS[z, m], m] (((-1 + m)^2 m z (-1 + m + z^2))/ Sqrt[z^2/(m + z^2)] + ((-1 + m)^2 m^2 (9 + m (-29 + 38 m)) + (-1 + m) m (-11 + m (66 + m (-152 + 119 m))) z^2 + (5 + m (-46 + m (158 + m (-248 + 139 m)))) z^4 + (-10 + m (47 + m (-94 + 73 m))) z^6 + (5 + 3 m (-4 + 5 m)) z^8) JacobiSN[InverseJacobiDS[z, m], m])))/(z (-1 + m + z^2)^3 (m + z^2)))

 Standard Form

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 MathML Form

 3 ds - 1 ( z m ) m 3 1 8 ( m - 1 ) 3 m 3 ( 1 z ( z 2 + m - 1 ) 3 ( z 2 + m ) ( m z cn ( ds - 1 ( z m ) m ) ( - ( m - 1 ) m z ( ( 3 m - 1 ) z 4 + ( m ( 8 m - 7 ) + 1 ) z 2 + ( m - 1 ) m ( 5 m - 2 ) ) - ( m - 1 ) ( z 2 + m - 1 ) z 2 z 2 + m ( - z 6 + ( 5 m - 3 ) z 4 + ( m ( 18 m - 19 ) + 4 ) z 2 + ( m - 1 ) m ( 12 m - 7 ) ) sn ( ds - 1 ( z m ) m ) + dn ( ds - 1 ( z m ) m ) ( m z ( z 2 + m - 1 ) ( m - 1 ) 2 z 2 z 2 + m + ( ( 3 m ( 5 m - 4 ) + 5 ) z 8 + ( m ( m ( 73 m - 94 ) + 47 ) - 10 ) z 6 + ( m ( m ( m ( 139 m - 248 ) + 158 ) - 46 ) + 5 ) z 4 + ( m - 1 ) m ( m ( m ( 119 m - 152 ) + 66 ) - 11 ) z 2 + ( m - 1 ) 2 m 2 ( m ( 38 m - 29 ) + 9 ) ) sn ( ds - 1 ( z m ) m ) ) ) - z ( z 2 + m - 1 ) 3 ( z 2 + m ) ( ( 23 ( m - 1 ) m + 8 ) E ( am ( ds - 1 ( z m ) m ) m ) + ( m - 1 ) ( 11 m - 7 ) F ( am ( ds - 1 ( z m ) m ) m ) ) ) - 15 ( m - 1 ) 3 ds - 1 ( z m ) ) m 3 InverseJacobiDS z m 1 8 m -1 3 m 3 -1 1 z z 2 m -1 3 z 2 m -1 m z JacobiCN InverseJacobiDS z m m -1 m -1 m z 3 m -1 z 4 m 8 m -7 1 z 2 m -1 m 5 m -2 -1 m -1 z 2 m -1 z 2 z 2 m -1 1 2 -1 z 6 5 m -3 z 4 m 18 m -19 4 z 2 m -1 m 12 m -7 JacobiSN InverseJacobiDS z m m JacobiDN InverseJacobiDS z m m m z z 2 m -1 m -1 2 z 2 z 2 m -1 1 2 -1 3 m 5 m -4 5 z 8 m m 73 m -94 47 -10 z 6 m m m 139 m -248 158 -46 5 z 4 m -1 m m m 119 m -152 66 -11 z 2 m -1 2 m 2 m 38 m -29 9 JacobiSN InverseJacobiDS z m m -1 z z 2 m -1 3 z 2 m 23 m -1 m 8 EllipticE JacobiAmplitude InverseJacobiDS z m m m m -1 11 m -7 EllipticF JacobiAmplitude InverseJacobiDS z m m m -1 15 m -1 3 InverseJacobiDS z m [/itex]

 Rule Form

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

 2007-05-02