A new continued fraction for Euler’s constant

Aldo Peretti
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 3, 1997, Number 1, Pages 23–34
Full paper (PDF, 344 Kb)

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Aldo Peretti
Facultad de Ciencia y Tecnologia – Universidad del Salvador
Rodriguez Peña 640
(1020) Buenos Aires, Argentina

Abstract

A new continued fraction is obtained for Euler constant C, namely:

    \[C = \frac{1}{2} - \frac{1}{3} = \Bigg \{ \frac{ \Big ( \frac{2r - 1}{r-1} \Big )^2 \mid }{ \mid \frac{-2^r + r}{r(r+1)} } + \frac{2^r + r \mid}{ \mid r^2} + r^2 \Big \{ \frac{(2^r + m)^2 \mid }{ \mid 1} \Big \}_{m=1}^{m=2^r - 1} \Bigg \}_{r = 2}^{r = \infty} \]

It is considered the possibility to prove the irrationality and transcendency of the constant by means of this expansion.

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Cite this paper

Peretti, A. (1997). A new continued fraction for Euler’s constant. Notes on Number Theory and Discrete Mathematics, 3(1), 23-34.

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