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InverseJacobiSD




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.47.20.0007.01









  


  








Input Form





D[InverseJacobiSD[z, m], {z, n}] == ((2^(-1 + n) Pi z^(-1 + n) (n - 1)! JacobiCN[InverseJacobiSD[z, m], m])/ (1 + (-1 + m) z^2)) Sum[(((m - 1)^(n - j - 1) m^j (1 + (m - 1) z^2)^(1 + j - n))/ ((1 + m z^2)^j (j! (n - j - 1)! Gamma[1/2 - j] Gamma[3/2 + j - n]))) Hypergeometric2F1[(1 - j)/2, -(j/2), 1/2 - j, 1 + 1/(m z^2)] Hypergeometric2F1[(2 + j - n)/2, (1 + j - n)/2, 3/2 + j - n, 1 + 1/((m - 1) z^2)], {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