D[InverseJacobiDN[z, m], {z, n}] == KroneckerDelta[n] InverseJacobiDN[z, m] - (JacobiCS[InverseJacobiDN[z, m], m]/(-1 + m + z^2)) Sum[(Pochhammer[1 - n, 2 (n - j) - 2]/((n - j - 1)! (2 z)^(n - 2 j - 1))) Sum[((-1)^(k + j) Binomial[j, k] Pochhammer[1/2, k] Pochhammer[1/2, j - k] (m - 1 + z^2)^(-j + k))/(1 - z^2)^k, {k, 0, j}], {j, 0, n - 1}] /; Element[n, Integers] && n >= 0

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2007-05-02