2025年12月22日 · If a function f has a pole at z_0, then the negative power part sum_ (j=-k)^ (-1)a_j (z-z_0)^j (1) of the Laurent series of f about z_0 sum_ (j=-k)^inftya_j (z-z_0)^j (2) is called …

Principal part In mathematics, the principal part has several independent meanings but usually refers to the negative-power portion of the Laurent series of a function.

= k= m + + 1 (z z0)m (z z0) is called the principal part of f (z) at z0. Easy fact: If g(z) has a zero of order m at z0, and f (z0) 6= 0, then f (z)=g(z) has a pole of order m at z0. Proof. Write g(z) = (z …

If a function f fails to be analytic at a point z 0 but is analytic at some point in every neighborhood of z 0, then z 0 is called a singular point, or singularity, of f

2023年1月1日 · From my knowledge, the principle part is the part of the Laurant series which's input goes from $-\infty$ to $0$. Thus my question is how did the paper find such a compact …

那么在这个区域之中我们可以将函数 f (z) 在点 z_ {o} 处展开为某个 级数 的形式（回想高数学过的 Taylor 公式），这个级数我们在复分析中称之为 洛朗级数 （ Laurent\quad series ） (仔细观察 …

z0 is a pole of order m 2 N if and only if there exists a function g analytic at z0 and g(z0) 6= 0 such that f(z) = (z z0) mg(z) locally, that is, for some neighborhood of z0.