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InverseJacobiCN






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseJacobiCN[z,m] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/09.38.20.0007.01









  


  










Input Form





D[InverseJacobiCN[z, m], {z, n}] == (-((2^(-1 + n) Pi z^(-1 + n) (-1 + n)! JacobiDS[InverseJacobiCN[z, m], m])/ (1 + m (-1 + z^2)))) Sum[(m^(n - j - 1) ((1 - m + m z^2)^(1 + j - n)/(j! (n - j - 1)! Gamma[1/2 - j] Gamma[3/2 + j - n])) Hypergeometric2F1[(1 - j)/2, -(j/2), 1/2 - j, 1 - 1/z^2] Hypergeometric2F1[(2 + j - n)/2, (1 + j - n)/2, 3/2 + j - n, 1 + (1 - m)/(m z^2)])/(z^2 - 1)^j, {j, 0, n - 1}] /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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