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Rational approximation to Euler's constant at a geometric rate of convergence


Authors: José A. Adell and Alberto Lekuona
Journal: Math. Comp. 89 (2020), 2553-2561
MSC (2010): Primary 11Y60; Secondary 60E05
DOI: https://doi.org/10.1090/mcom/3528
Published electronically: February 20, 2020
MathSciNet review: 4109578
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Abstract: We give a rational approximation to Euler's constant at a geometric rate of convergence, which is easy to compute. Moreover, such an approximation is completely monotonic. The approximants are built up in terms of expectations of the harmonic numbers acting on the standard Poisson process.


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Additional Information

José A. Adell
Affiliation: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: adell@unizar.es

Alberto Lekuona
Affiliation: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
Email: lekuona@unizar.es

DOI: https://doi.org/10.1090/mcom/3528
Keywords: Euler's constant, fast computation, rational approximation, harmonic numbers, Poisson process.
Received by editor(s): January 16, 2019
Received by editor(s) in revised form: November 20, 2019, and January 13, 2020
Published electronically: February 20, 2020
Additional Notes: The authors were partially supported by Research Projects DGA (E-64)and MTM2015-67006-P. The first author is the corresponding author.
Article copyright: © Copyright 2020 American Mathematical Society