On partial fraction expansion for meromorphic functions

L. S. Maergoiz

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 3, pp. 487-492

Résumé

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.