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ЖУРНАЛЫ // Журнал математической физики, анализа, геометрии // Архив

Матем. физ., анал., геом., 2002, том 9, номер 3, страницы 487–492 (Mi jmag311)

Эта публикация цитируется в 3 статьях

On partial fraction expansion for meromorphic functions

L. S. Maergoiz

Krasnoyarsk State Architecture and Civil Engineering, Academy 82 Svobodny Ave., Krasnoyarsk, 660041, Russia

Аннотация: 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.

MSC: 30D15

Поступила в редакцию: 01.12.2001

Язык публикации: английский



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