Abstract
The Stokes lines for Г(
z
) are the positive and negative imaginary axes, where all terms in the divergent asymptotic expansion for In Г(
z
) have the same phase. On crossing these lines from the right to the left half-plane, infinitely many subdominant exponentials appear, rather than the usual one. The exponentials increase in magnitude towards the negative real axis (anti-Stokes line), where they add to produce the poles of Г(
z
). Corresponding to each small exponential is a separate component asymptotic series in the expansion for In Г(
z
). If each is truncated near its least term, its exponential switches on smoothly across the Stokes lines according to the universal error-function law. By appropriate subtractions from In Г(
z
), the switching-on of successively smaller exponentials can be revealed. The procedure is illustrated by numerical computations.
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