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.
References in periodicals archive ?
He starts with Cauchy-Riemann equations in the introduction, then proceeds to power series, results on holomorphic functions, logarithms, winding numbers, Couchy's theorem, counting zeros and the open mapping theorem, Eulers formula for sin(z), inverses of holomorphic maps, conformal mappings, normal families and the Riemann mapping theorem, harmonic functions, simply connected open sets, Runge's theorem and the Mittag-Leffler theorem, the Weierstrass factorization theorem, Caratheodory's theorem, analytic continuation, orientation, the modular function, and the promised Picard theorems.