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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2002, Volume 9, Number 3, Pages 487–492
(Mi jmag311)
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This article is cited in 3 scientific papers (total in 3 papers)
On partial fraction expansion for meromorphic functions
L. S. Maergoiz Krasnoyarsk State Architecture and Civil Engineering, Academy 82 Svobodny Ave., Krasnoyarsk, 660041, Russia
Abstract:
The paper is a short survey of results devoted to partial fraction expansion for meromorphic functions of one complex variable. In particular, this contains new results by the author on representation of a meromorphic function $\Phi$ on $\mathbb C$ in the form
$$
\Phi(z)=\lim_{R\to\infty}\sum_{|b_k|<R}\Phi_k(z)+\alpha(z),
$$
where $\{b_k\}_1^\infty$ is the sequence of all its poles arranged in the order of increase of the absolute values and tending to $\infty$,
$$
\biggl\{\Phi_k(z)=\sum_{n=1}^{N_k}\frac{A_{k,n}}{(z-b_k)^n},\ k=1,2,\dots\biggr\}
$$
is the sequence of principal parts of the Laurent expansion of $\Phi$ near the poles, and $\alpha$ is an entire function.
Received: 01.12.2001
Citation:
L. S. Maergoiz, “On partial fraction expansion for meromorphic functions”, Mat. Fiz. Anal. Geom., 9:3 (2002), 487–492
Linking options:
https://www.mathnet.ru/eng/jmag311 https://www.mathnet.ru/eng/jmag/v9/i3/p487
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