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JacobiZeta






Mathematica Notation

Traditional Notation









Elliptic Integrals > JacobiZeta[z,m] > Differentiation > Low-order differentiation > With respect to m





http://functions.wolfram.com/08.07.20.0004.01









  


  










Input Form





D[JacobiZeta[z, m], {m, 2}] == ((1/2) (m - 1) m (2 - m + m Cos[2 z]) EllipticK[m]^2 (Sin[2 z] - 2 JacobiZeta[z, m] Sqrt[1 - m Sin[z]^2]) - (2 - m + m Cos[2 z]) EllipticE[m]^2 (m Sin[2 z] - 2 JacobiZeta[z, m] Sqrt[1 - m Sin[z]^2]) - EllipticE[m] EllipticK[m] ((-m) (3 - 2 m + m Cos[2 z]) Sin[2 z] + 4 JacobiZeta[z, m] (1 - m Sin[z]^2)^(3/2)))/(8 (m - 1)^2 m^2 EllipticK[m]^2 (1 - m Sin[z]^2)^(3/2))










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