New series involving binomial coefficients (II)

2023/07/06 by Sun, Zhi-Wei · 2 citations
#05A19 #11A07 #11B65 #11B68 #33B15 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2307.03086

Abstract

In this paper, we evaluate some series of the form ∑_k=1^∞\fracak²+bk+ck(3k-1)(3k-2)m^k\binom4kk. For example, we prove that ∑_k=1^∞\frac(5k²-4k+1)8^kk(3k-1)(3k-2)\binom4kk=\frac32π and ∑_k=1^∞\frac415k²-343k+62k(3k-1)(3k-2)(-8)^k\binom4kk=-3log2. We also pose many new conjectural series identities involving binomial coefficients; for example, we conjecture that ∑_k=0^∞\frac\binom2kk³4096^k(9(42k+5)∑_0≤ j

Cited by

• Analytic Dilogarithm Identities
• Various irrational series involving binomial coefficients

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