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Date: 22-11-2018
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Date: 22-11-2018
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If a function analytic at the origin has no singularities other than poles for finite , and if we can choose a sequence of contours about tending to infinity such that never exceeds a given quantity on any of these contours and is uniformly bounded on them, then
where is the sum of the principal parts of at all poles within . If there is a pole at , then we can replace by the negative powers and the constant term in the Laurent series of about .
REFERENCES:
Jeffreys, H. and Jeffreys, B. S. "Mittag-Leffler's Theorem." §12.006 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 383-386, 1988.
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