$ζ(5)$的一个三阶类递归
A third-order Apery-like recursion for $ζ(5)$
摘要：
在1978年，阿斯塔纳给出了序列的有理逼近$ζ(2)$和$ζ(3)$产生的非理性的每一个这些数字。其中一个关键成分的阿塞尔的证明是二阶差分方程的多项式系数满足上述近似的分子和乘数。最近，一个类似的二阶差分方程的$ζ(4)$已被发现。该注释包含了上述结果对于数$ζ(5)$的可能推广。
英文摘要：
In 1978, Apery has given sequences of rational approximations to $ζ(2)$ and $ζ(3)$ yielding the irrationality of each of these numbers. One of the key ingredient of Apery's proof are second-order difference equations with polynomial coefficients satisfied by numerators and denominators of the above approximations. Recently, a similar second-order difference equation for $ζ(4)$ has been discovered. The note contains a possible generalization of the above results for the number $ζ(5)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
