正せい則そく関かん数すう

せ

い

そ

く

か

ん

す

う

Meanings

1

noun

holomorphic function

mathematics

Mathematical term for a complex-valued function that is complex differentiable in a neighborhood of every point in its domain. Equivalent to an analytic function in complex analysis.

正せい則そく関かん数すうは複ふく素そ平へい面めんの開

かい

集しゅう

合ごう

上じょう

で

定てい

義ぎ

さ

れる

。

A holomorphic function is defined on an open set of the complex plane.

コーシーの積せき分ぶん定てい理りは正せい則そく関かん数すうの重じゅう要ような性せい質しつを示しめす。

Cauchy's integral theorem demonstrates an important property of holomorphic functions.

Kanji

正correct, justice, righteous
則rule, law, follow
関connection, barrier, gateway
数number, strength, fate

Related words

解かい析せき関かん数すう
In complex analysis, 解析関数 is synonymous with 正則関数; both refer to functions that are locally given by a convergent power series. In broader contexts, 解析関数 may also refer to real analytic functions.
複ふく素そ関かん数すう
複素関数 is a more general term for any complex-valued function, not necessarily holomorphic. 正則関数 is a subset of 複素関数 that satisfies differentiability conditions.

Built from

正せい則そく+関かん数すう

Etymology

Compound of 正則 (regular, proper) and 関数 (function). The term is a direct calque from the mathematical concept of a holomorphic (regular) function in complex analysis.