EllipticE[z, m] == (-1)^Round[Re[z]/Pi] Sin[z] HypergeometricPFQ[{{1/2}, {1/2}, {-(1/2)}}, {{3/2}, {}, {}}, Sin[z]^2, m Sin[z]^2] + 2 Round[Re[z]/Pi] EllipticE[m]

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2001-10-29