🚀 go-pugleaf

RetroBBS NetNews Server

Inspired by RockSolid Light RIP Retro Guy

Article View: fj.sci.math
Article #13782

Re: Pi kouski-shyu

#13782
From: Matumoto Ryuji Ryuji
Date: Mon, 27 May 1996 00:00
53 lines
2396 bytes
$B>>85N4Fs!wCNG=!&6e=#9)6HBg3X$G$9!%(B

$B<+8J%U%)%m!<$G$9!%(B

<4o9sga$9a9@ai.ai.kyutech.ac.jp>$B$N5-;v$K$*$$$F(B
ryuji@donald.ai.kyutech.ac.jp$B$5$s$O=q$-$^$7$?!#(B

>> $B>>85N4Fs!wCNG=!&6e=#9)6HBg3X$G$9!%(B
>> 
>> $B1_<~N($N8x<0=8$r:n$j$^$7$?!%(B
>> 
>> http://www.pluto.ai.kyutech.ac.jp/plt/matumoto/syumi.html
>> 
>> $B$K$"$k$N$G$I$&$>!%?t<0$,$9$Y$F2hA|%U%!%$%k$GF~$C$F$$$^$9$N$G(B
>> $B%M%C%H%o!<%/$,:Y$$?M$O8+$k$N;_$a$?$[$&$,$$$$$G$9$h!%(B

$B$3$N8x<0=8$G$9$,!$4V0c$$$,4v$D$bH/8+$5$l$^$7$?!%%a!<%k$G$b;XE&(B
$B$5$l$^$7$?!%(B($B;XE&$7$F2<$5$C$?J}$"$j$,$H$&$4$6$$$^$9!%(B)

$B8=:_2~Dj:n6H$7$F$$$^$9$N$G!$$9$_$^$;$s!%(B

$B$^$?!$0J2<$N<0$b4V0c$C$F$$$^$9!%(B

> -----------------------------------------
> \subsection{The Quartic AGM: by J.M.Borwein and P.B.Borwein}
> $B$O$8$a$K(B$a_0 := 1$, $b_0 := \sqrt{\sqrt{1/2}}$$B$HCV$/!%(B
> $B<!$N?tNs$r7W;;$9$k!%(B
> $$a_{n+1} := \frac{a_n + b_n}{2}$$
> $$b_{n+1} := \sqrt[4]{\frac{a_n b_n (a_n^2 + b_n^2)}{2}}$$
> $B$3$N?tNs$O!$(B4$B<!$N<}B+$r<($7!$(B
> $\lim_{n \rightarrow \infty} a_n = \lim_{n \rightarrow \infty} b_n$$B$H$J$k!%(B
> 
> $B<!$N?tNs$rDj5A$9$k!%(B
> $$\pi_n = \frac{2 a_{n+1}^4}{\displaystyle 1-\sum_{k=0}^{n} 4^n[a_k^4 - (\frac{a_k^2 + b_k^2}{2})^2]}$$
> $\pi_n$$B$O(B$\pi$$B$K<}B+$9$k!%(B
> -----------------------------------------

$B$K$*$$$F!$(B

$$\pi_n = \frac{2 a_{n+1}^4}{\displaystyle 1-\sum_{k=0}^{n} 4^n[a_k^4 - (\frac{a_k^2 + b_k^2}{2})^2]}$$

$B$O4V0c$$$G!$(B

$$\pi_n = \frac{2 a_{n+1}^4}{\displaystyle 1-\sum_{k=0}^{n} 4^k[a_k^4 - (\frac{a_k^2 + b_k^2}{2})^2]}$$

$B$,@52r$G$9!%(B ($B$^$"!$?t<0$K6/$$J}$J$i!$85$N$^$^$@$H(B4^n$B$,$/$/$j=P$7$,(B
$B=PMh$^$9$N$G!$<0$,4V0c$C$F$$$k$N$G$O$J$$$+$H4*$E$+$l$k$+$b$7$l$^$;(B
$B$s$,!%(B)
---------------------------
Ryuji Matsumoto
Kyushu Institute of Technology.(Japan)
e-mail:matumoto@pluto.ai.kyutech.ac.jp
Technical Details
Message-ID: <4oarae$ip6@ai.ai.kyutech.ac.jp>
Path: arc1-ca.pugleaf.net!unknown!not-for-mail
References: <4o9sga$9a9@ai.ai.kyutech.ac.jp>

Show Full Headers
Complete Article Headers
X-Google-Language: Japanese,JIS
X-Google-Thread: f4956,db95f269525731a2,start
X-Google-Attributes: gidf4956,public
From: ryuji@donald.ai.kyutech.ac.jp (Matumoto Ryuji Ryuji)
Subject: Re: Pi kouski-shyu
Date: 1996/05/27
Message-ID: <4oarae$ip6@ai.ai.kyutech.ac.jp>
X-Deja-AN: 156885447
distribution: fj
references: <4o9sga$9a9@ai.ai.kyutech.ac.jp>
organization: Kyushu Institute of Technology, AI Dept, Iizuka, JAPAN.
newsgroups: fj.sci.math