EllipticTheta[1, z, q] \[Proportional] Exp[((Pi I)/2) Floor[Arg[q - x]/(2 Pi)]] (EllipticTheta[1, z, x] + Derivative[0, 0, 1][EllipticTheta][1, z, x] (q - x) + (1/2) Derivative[0, 0, 2][EllipticTheta][1, z, x] (q - x)^2 + (1/6) Derivative[0, 0, 3][EllipticTheta][1, z, x] (q - x)^3 + O[(q - x)^4]) /; Element[x, Reals] && -1 < x < 0

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2007-05-02