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Mittag-Leffler's theorem
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(Theorem)
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Let $G$ be an open subset of $\mathbb{C}$ let $\{a_k\}$ be a sequence of distinct points in $G$ which has no limit point in $G$ For each $k$ let $A_{1k},\dots,A_{m_kk}$ be arbitrary complex coefficients, and define $$S_k(z) = \sum_{j=1}^{m_k} \frac{A_{jk}}{(z-a_k)^j}.$$ Then there exists a meromorphic function $f$ on $G$ whose poles are exactly the points $\{a_k\}$ and such that the singular part of $f$ at $a_k$ is $S_k(z)$ for each $k$
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"Mittag-Leffler's theorem" is owned by Koro.
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Cross-references: singular, poles, function, meromorphic, coefficients, complex, limit point, points, sequence, open subset
There is 1 reference to this entry.
This is version 1 of Mittag-Leffler's theorem, born on 2002-12-11.
Object id is 3732, canonical name is MittagLefflersTheorem.
Accessed 4991 times total.
Classification:
| AMS MSC: | 30D30 (Functions of a complex variable :: Entire and meromorphic functions, and related topics :: Meromorphic functions, general theory) |
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Pending Errata and Addenda
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