论文标题
有两个涉及弗兰内尔数字的一致性
On two congruences involving Franel numbers
论文作者
论文摘要
通过符号求和方法，我们为$π^2 $：\ begin {align*} \ sum_ {k = 1}^\ infty \ frac {h_k-2h_ {2k}} {（ - 3） $ h_k = \ sum_ {j = 1}^k 1/j $。我们还得出了与本系列相关的$ P $ ADIC一致性。作为应用程序，我们证明了涉及弗拉内尔数字的两个一致性，其中一个最初是由太阳猜想的。
Via symbolic summation method, we establish the following series for $π^2$: \begin{align*} \sum_{k=1}^\infty \frac{H_k-2H_{2k}}{(-3)^k k} = \frac{π^2}{18}, \end{align*} where $H_k=\sum_{j=1}^k 1/j$. We also derive a $p$-adic congruence related to this series. As an application, we prove two congruences involving Franel numbers, one of which was originally conjectured by Sun.
