A new series for $\pi^3$ and related congruences
By Zhi-Wei Sun. 2010
63 citations recorded by the source corpus.
Let denote the second-order harmonic number for n = 0, 1, 2, …. In this paper we obtain the following identity: We explain how we found the series and develop related congruences involving Bernoulli or Euler numbers; for example, it is shown that for any prime p > 3, where E0, E1, E2, … are Euler numbers. Motivated by the Amdeberhan–Zeilberger identity , we also establish the congruence for each prime p > 3.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/c668b99feafc1090bdbbd6bc7b63fc62adfca1ba
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Congruences for central binomial sums and finite polylogarithms (2010, result): “polylogarithms and evaluate the sums (2) for t ∈ {1,−1,2,3,4,−1/2} and d = 0,1,2. Some special cases of the second type of sum in Equation (2), and other related sums, were considered by Z. W. Sun in [16], with attention to a comparison with the corresponding infinite sums. As we explain in our Secti”