Semi-automated proof of supercongruences on partial sums of hypergeometric series
Semi-automated proof of supercongruences on partial sums of hypergeometric series
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DOI：
10.1016/j.jsc.2018.06.004
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Ji-Cai Liu
中科院分区：
文献类型：
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作者：
Ji-Cai Liu
利用Schneider开发的Sigma软件包，自动发现并证明了一些涉及调和数的组合恒等式，并由此导出了超几何级数部分和的超同余式.这些结果证实了Guo（2017）最近提出的货车Hamme超同余在某些特殊情况下的一些代数推广.
Using the software packageSigmadeveloped by Schneider, we automatically discover and prove some combinatorial identities involving harmonic numbers, from which we deduce some supercongruences on partial sums of hypergeometric series. These results confirm some conjectural generalizations of van Hamme's supercongruences in some special cases, which were recently proposed by Guo (2017).