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From: chiaki@kit.ac.jp (Tsukamoto Chiaki)
Newsgroups: fj.sci.math
Subject: Re: ζ(s),DL(s,χ),_{amodN(s)},ζ(s,x)の複素平面上での正則性・有理型性・解析接続可能性の証明
Date: Fri, 27 Jul 2012 09:55:19 GMT
Organization: Kyoto Institute of Technology
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工繊大の塚本です.

In article <jupqf3$eq2$1@dont-email.me>
"Kyoko Yoshida" <kyokoyoshida123@gmail.com> writes:
> In article <120725205714.M0117169@ras1.kit.ac.jp>
> Tsukamoto Chiaki <chiaki@kit.ac.jp> wrtites:
> > 簡単にいえば, 収束半径の公式中で
> >  \limsup_{n \to \infty} (|a_n|)^{1/n}
> >   = \limsup_{n \to \infty} (|a_{n+1}|)^{1/n}
> > となるからです.

 \sum_{n=0}^\infty a_n z^n と \sum_{n=0}^\infty a_{n+1} z^n の
収束半径が一致することを認めるなら,

> http://www.geocities.jp/sayori_765195/prop192_1202__06.jpg
> http://www.geocities.jp/sayori_765195/prop192_1202__04.jpg
> でいいのですね。

そういうことです.
-- 
塚本千秋@数理・自然部門.基盤科学系.京都工芸繊維大学
Tsukamoto, C. : chiaki@kit.ac.jp