Abstract

A new root and ratio test for bicomplex power series produces the bicomplex extension theorem, where any complex power series with positive radius of convergence R extends, via a simple change of the complex domain variable z to the bicomplex variable $\zeta$, to a bicomplex function analytic in a four real-dimensional ball with the same positive radius R. In this way, any complex-analytic function has a natural extension to a bicomplex-analytic function.

中文翻译：

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范数的比较：双复根和比率检验以及扩展定理

摘要

双复幂级数的新根和比率检验产生双复扩展定理，其中任何具有正收敛半径R 的复幂级数通过将复域变量z简单更改为双复变量来扩展$\zeta$, 到具有相同正半径R的四实维球中的双复函数解析。这样，任何复解析函数都具有双复解析函数的自然扩展。