EllipticTheta[1, z, q] == Exp[((Pi I)/2) Floor[Arg[q - x]/(2 Pi)]] Sum[(Derivative[0, 0, k][EllipticTheta][1, z, x]/k!) (q - x)^k, {k, 0, Infinity}] /; Element[x, Reals] && -1 < x < 0

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2007-05-02