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 atz=z_i, having orderm_iand principal partsthe formula iswhere thep_i(z) are polynomials,g(z) is an entire function, and the series converges uniformly in every bounded region where ƒ(z) is analytic.

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