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variants of this functions
EllipticPi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/08.06.20.0006.01









  


  










Input Form





D[EllipticPi[n, z, m], {m, 2}] == ((4 m^2 - n - m (2 + n))/(4 (m - 1)^2 m (m - n)^2)) EllipticE[z, m] + (1/(4 (m - 1) m (m - n))) EllipticF[z, m] + (3/(4 (m - n)^2)) EllipticPi[n, z, m] + ((m - 3 m^2 + 2 n + m (4 m^2 - n - m (2 + n)) Sin[z]^2) Sin[2 z])/ (8 (m - 1)^2 (m - n)^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