论文标题
通过Zudilin-Straub t-Transform探索一般的Apéry限制
Exploring General Apéry Limits via the Zudilin-Straub t-transform
论文作者
论文摘要
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 Apéry limits.在获得我们所谓的“主要猿猴奇迹”时，相关常数（即所谓的猿人限制）证明了不合理性非常罕见，我们每次都会获得至少“次要常数”，即明显的常数，即在某些expection seperienceapérience的限制中，将其定义为某些明确的限制，即某些明确的限制，即某些eprienceapérence的限制，这些序列是apérence的限制，是一种限制，apérence的限制是，apérence的限制是，apérence的限制是apérence的限制。该常数的计算，具有指数衰减的误差。
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 Apéry limits. While getting what we call "major Apéry miracles", proving irrationality of the associated constants (i.e. the so-called Apéry limits) is very rare, we do get, every time, at least a "minor Apéry miracle" where an explicit constant, defined as an (extremely slowly-converging) limit of some explicit sequence, is expressed as an Apéry limit of some recurrence, with some initial conditions, thus enabling a very fast computation of that constant, with exponentially decaying error.
