论文标题
从实验发现的高几幅递归获得的串联加速公式
Series acceleration formulas obtained from experimentally discovered hypergeometric recursions
论文作者
论文摘要
2010年，KH。 Hessami Pilehrood和T. hessami Pilehrood引入了生成功能身份，用于通过Markov-Wilf-Zeilberger方法获得Dirichlet $β$函数值的串联加速度。受这些过去结果的启发，以及Chu等人介绍的相关结果，我们引入了各种超测量复发。我们使用WZ方法证明了这些复发，并应用这些复发以获得串联加速身份。我们介绍了一个概括的一系列总结，以概括了$ \ frac {1} {1} {π^2} $的ramanujan型系列，这是由于吉利拉（Guillera）而导致的，以及一个由lupaş导致的加速度的加速度系列的总结，以及许多相关结果。
In 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function identities used to obtain series accelerations for values of Dirichlet's $β$ function, via the Markov--Wilf--Zeilberger method. Inspired by these past results, together with related results introduced by Chu et al., we introduce a variety of hypergeometric recurrences. We prove these recurrences using the WZ method, and we apply these recurrences to obtain series acceleration identities. We introduce a family of summations generalizing a Ramanujan-type series for $\frac{1}{π^2}$ due to Guillera, and a family of summations generalizing an accelerated series for Catalan's constant due to Lupaş, and many related results.
