Mittag-Leffler's theorem


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.