• Corpus ID: 115173388

New proofs of some formulas of Guillera-Ser-Sondow

  title={New proofs of some formulas of Guillera-Ser-Sondow},
  author={Vassily Bolbachan},
  journal={arXiv: Number Theory},
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. 

Three Notes on Ser's and Hasse's Representations for the Zeta-functions

This paper shows that the famous Hasse's series for the zeta-function is equivalent to an earlier expression given by a little-known French mathematician Joseph Ser in 1926, and shows that there exist numerous series of the same nature.

Rational approximants for the Euler-Gompertz constant

We obtain two sequences of rational numbers which converge to the Euler-Gompertz constant. Denote by the integral of f(x)e^{-x} from 0 to infinity. Recall that the Euler-Gompertz constant \delta is .

An Explicit Identity of Sums of Powers of Complex Functions to Prove Riemann Hypothesis

This paper presents an absolutely explicit identity for solving sums of powers of complex functions with out one sum depends on the others. Via this sums of powers of complex functions, this paper



A Faster Product for π and a New Integral for In

  • J. Sondow
  • Mathematics, Computer Science
    Am. Math. Mon.
  • 2005
1. N. Bernstein, Démonstration du théorème de Weierstrass fondée sur le calcul de probabilité, Proc.

Problem 11381

Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent

The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and of the second author for Euler’s constant γ and its alternating analog

An Infinite Product for e γ via Hypergeometric Formulas for Euler's Constant γ

    Sur une expression de la fonction ζ (s) de Riemann

    • Comptes Rendus
    • 1926