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On Rational Approximations to Euler's Constant γ and to γ+log(ab)
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-06-28
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
The author continues to study series transformations for the Euler-Mascheroni constant γ.
Here, we discuss in detail recently published results of A.
I.
Aptekarev and T.
Rivoal who found rational approximations to γ and γ+logq (q∈ℚ>0) defined by linear recurrence formulae.
The main purpose of this paper is to adapt the concept of linear series transformations with integral coefficients such that rationals are given by explicit formulae which approximate γ and γ+logq.
It is shown that for every q∈ℚ>0 and every integer d≥42 there are infinitely many rationals am/bm for m=1,2,… such that |γ+logq−am/bm|≪((1−1/d)d/(d−1)4d)m and bm∣Zm with logZm~12d2m2 for m tending to infinity.
American Psychological Association (APA)
Elsner, Carsten. 2009. On Rational Approximations to Euler's Constant γ and to γ+log(ab). International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-22.
https://search.emarefa.net/detail/BIM-486218
Modern Language Association (MLA)
Elsner, Carsten. On Rational Approximations to Euler's Constant γ and to γ+log(ab). International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-22.
https://search.emarefa.net/detail/BIM-486218
American Medical Association (AMA)
Elsner, Carsten. On Rational Approximations to Euler's Constant γ and to γ+log(ab). International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-22.
https://search.emarefa.net/detail/BIM-486218
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-486218