2023/10/05 by Qing-Hu Hou, Zhi‐Wei Sun, Hou, Qing-Hu +1
Mathematics · #11B65 #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A19 #Secondary 33B15
paper · pdf · doi:10.48550/arxiv.2310.03699
openalex publication_date 2023/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
During 2022--2023 Z.-W. Sun posed many conjectures on infinite series with summands involving generalized harmonic numbers. Motivated by this, we deduce 58 series identities involving harmonic numbers, eight of which were previously conjectured by the second author. For example, we obtain that ∑k=1∞ \frac(-1)kk22k \choose k3k \choose k ( (7 k-2)/(2 k-1) Hk-1(2)-(3)/(4 k2) ) = (π4)/(720). and ∑k=1^∞ \frac1k2 2k \choose k2 ( (30k-11)/(k(2k-1)) (H2k-1(3) + 2 Hk-1(3)) + (27)/(8k4) ) = 4 ζ(3)2, where Hn(m) denotes ∑_0