New proofs of some formulas of Guillera-Ser-Sondow

Abstract

We present logarithmic series for u, ln u and the Euler-Mascheroni constant gamma. It was indicated by J. Sondow that Theorem 4 and all proofs are new. All proofs are elementary. We present some conjectures.

arXiv comment6 pages, new results added, no figures

Cited by in corpus (2)

• Closed-form formula of Riemann zeta function and eta function for all non-zero given complex numbers via sums of powers of complex functions to disprove Riemann Hypothesis
• Rational approximants for the Euler-Gompertz constant