Mittag-Leffler's theorem


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Mittag-Leffler's theorem

[′mi‚täk ′lef·lərz ‚thir·əm]
(mathematics)
A theorem that enables one to explicitly write down a formula for a meromorphic complex function with given poles; for a function ƒ(z) with poles at z = zi , having order mi and principal parts the formula is where the pi (z) are polynomials, g (z) is an entire function, and the series converges uniformly in every bounded region where ƒ(z) is analytic.