arXiv math/05080422005-08-01math.NTmath.CA

New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi)

Jonathan Sondow

备注：: 6 pages, submitted for publication, presented at the XXIVth Journeés Arithmetiques in Marseilles
发表信息：: Additive Number Theory, Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson (D. Chudnovsky and G. Chudnovsky, eds.), Springer, 2010

英文摘要：

In math.CA/0211148 we observed that $\ln(4/ π)$ is an "alternating" analog of Euler's constant $γ$. Here we use the binary expansion of an integer to give a rational series for $\ln(4/ π)$ analogous to Vacca's series for $γ$. Also, using a known generalization of Vacca's series to other bases, we accelerate Addison's series for $γ$. Along the way, we give new proofs of Vacca's and Addison's formulas.

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