D[JacobiSD[z, m], {m, 2}] == (1/(4 (-1 + m)^2 m^2)) ((-1 + m) ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m]) JacobiND[z, m]^2 ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m] - m JacobiDN[z, m] JacobiSC[z, m]) JacobiSD[z, m] + m JacobiCD[z, m]^2 ((((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m])^ 2 - (1 + m) ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m]) JacobiDN[z, m] JacobiSC[z, m] + m JacobiDN[z, m]^2 JacobiSC[z, m]^2) JacobiSD[z, m] + m JacobiDC[z, m] JacobiDN[z, m] JacobiNC[z, m] JacobiND[z, m] JacobiSN[z, m]) + JacobiCD[z, m] JacobiND[z, m] (-2 z + 4 m z - 2 m^2 z + EllipticE[JacobiAmplitude[z, m], m] - 3 m EllipticE[JacobiAmplitude[z, m], m] + EllipticF[JacobiAmplitude[z, m], m] - m EllipticF[JacobiAmplitude[z, m], m] - m ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m]) JacobiDC[z, m] JacobiDN[z, m] JacobiNC[z, m] - m^2 z JacobiCN[z, m] JacobiSC[z, m] JacobiSN[z, m] + m^3 z JacobiCN[z, m] JacobiSC[z, m] JacobiSN[z, m] + m^2 EllipticE[JacobiAmplitude[z, m], m] JacobiCN[z, m] JacobiSC[z, m] JacobiSN[z, m] - m JacobiCN[z, m] JacobiSN[z, m] Sqrt[1 - m JacobiSN[z, m]^2] + JacobiDN[z, m] (2 m^2 JacobiSC[z, m] - m^2 JacobiCN[z, m] JacobiSC[z, m]^2 JacobiSN[z, m] + ((-1 + m) z + EllipticE[JacobiAmplitude[z, m], m]) Sqrt[1 - m JacobiSN[z, m]^2])))

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2001-10-29