Inspired by a recent beautiful construction of Armin Straub and Wadim Zudilin, that 'tweaked' the sum of the $s^{th}$ powers of the $n$-th row of Pascal's triangle, getting instead of sequences of numbers, sequences of rational functions, we do the same for general binomial coefficients sums, getting a practically unlimited supply of Ap\'ery limits. While getting what we call "major Ap\'ery miracles", proving irrationality of the associated constants (i.e. the so-called Ap\'ery limits) is very rare, we do get, every time, at least a "minor Ap\'ery miracle" where an explicit constant, defined as an (extremely slowly-converging) limit of some explicit sequence, is expressed as an Ap\'ery limit of some recurrence, with some initial conditions, thus enabling a very fast computation of that constant, with exponentially decaying error.
翻译：受最近阿敏斯特劳布和瓦迪姆祖迪林的美丽构造的启发,“tweaked” the gun of $s_th} gun of the $s_th_th_rights of $n $th_th_rights of Pascal's criends, 代替数字序列, 理性函数序列, 我们对于一般的二进制系数数也这样做, 获得几乎无限的Ap\'ery限制。 当我们得到我们所谓的“ major Ap\'er miracles”, 证明相关常数( 所谓的Ap\'er limit) 不合理性非常罕见的时候, 我们确实每次都得到, 至少是一个“ minor Ap\'er miray miracil” 奇迹, 被定义为某些明确序列的( 极为缓慢的) 限制, 以某些初始条件表示为Ap\'rest of some a print recess recre recess recess, as a fear a for a for a for covention.
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