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

Adell, José; Lekuona, Alberto

doi:10.1090/mcom/3528

Rational approximation to Euler’s constant at a geometric rate of convergence
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by José A. Adell and Alberto Lekuona HTML | PDF

Math. Comp. 89 (2020), 2553-2561 Request permission

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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