"아페리(Apéry) 점화식"의 두 판 사이의 차이
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==개요== | ==개요== | ||
* [[Ζ(3)는 무리수이다(아페리의 정리)]]의 증명에서 등장한 점화식 | * [[Ζ(3)는 무리수이다(아페리의 정리)]]의 증명에서 등장한 점화식 | ||
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| + | ==점화식== | ||
| + | * $n^2 u_{n}-(An^2-An+\lambda)u_{n-1}+B(n-1)^2u_{n-2}=0$ | ||
| + | * $n^2 u_{n}-(7n^2-7n+2)u_{n-1}+8(n-1)^2u_{n-2}=0$ | ||
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| + | ==관련된 항목들== | ||
| + | * [[점근 급수(asymptotic series)]] | ||
==관련 논문== | ==관련 논문== | ||
* Don Zagier, [http://people.mpim-bonn.mpg.de/zagier/files/tex/AperylikeRecEqs/fulltext.pdf Integral solutions of Apéry-like recurrence equations] | * Don Zagier, [http://people.mpim-bonn.mpg.de/zagier/files/tex/AperylikeRecEqs/fulltext.pdf Integral solutions of Apéry-like recurrence equations] | ||
| + | * McIntosh, Richard J. 1996. “An Asymptotic Formula for Binomial Sums.” Journal of Number Theory 58 (1) (May): 158–172. doi:10.1006/jnth.1996.0072. | ||
| + | * Wimp, Jet, and Doron Zeilberger. 1985. “Resurrecting the Asymptotics of Linear Recurrences.” Journal of Mathematical Analysis and Applications 111 (1) (October): 162–176. doi:10.1016/0022-247X(85)90209-4. | ||
* A. van der Poorten [http://dx.doi.org/10.1007/FBF03028234 A proof that Euler missed ... Apéry's Proof of the irrationality of $\zeta(3)$], The Mathematical Intelligencer 1 (4): 195-203, 1979 | * A. van der Poorten [http://dx.doi.org/10.1007/FBF03028234 A proof that Euler missed ... Apéry's Proof of the irrationality of $\zeta(3)$], The Mathematical Intelligencer 1 (4): 195-203, 1979 | ||
** http://jones.math.unibas.ch/~massierer/algebra-hs11/vanderPoorten2.pdf | ** http://jones.math.unibas.ch/~massierer/algebra-hs11/vanderPoorten2.pdf | ||
2013년 3월 27일 (수) 15:28 판
개요
- Ζ(3)는 무리수이다(아페리의 정리)의 증명에서 등장한 점화식
점화식
- $n^2 u_{n}-(An^2-An+\lambda)u_{n-1}+B(n-1)^2u_{n-2}=0$
- $n^2 u_{n}-(7n^2-7n+2)u_{n-1}+8(n-1)^2u_{n-2}=0$
관련된 항목들
관련 논문
- Don Zagier, Integral solutions of Apéry-like recurrence equations
- McIntosh, Richard J. 1996. “An Asymptotic Formula for Binomial Sums.” Journal of Number Theory 58 (1) (May): 158–172. doi:10.1006/jnth.1996.0072.
- Wimp, Jet, and Doron Zeilberger. 1985. “Resurrecting the Asymptotics of Linear Recurrences.” Journal of Mathematical Analysis and Applications 111 (1) (October): 162–176. doi:10.1016/0022-247X(85)90209-4.
- A. van der Poorten A proof that Euler missed ... Apéry's Proof of the irrationality of $\zeta(3)$, The Mathematical Intelligencer 1 (4): 195-203, 1979