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Liu, Songhao; Lu, Dawei

Improved convergence towards Glaisher-Kinkelin’s and Bendersky-Adamchik’s constants. (English) Zbl 1421.11106

Result. Math. 71, No. 3-4, 731-747 (2017).
Summary: In this paper, some new continued fraction approximations, inequalities and rates of convergence of Glaisher-Kinkelin’s and Bendersky-Adamchik’s constants are provided. To demonstrate the superiority of our new convergent sequences over the classical sequences and Mortici’s sequences, some numerical computations are also given at the end of this paper.

MSC:

11Y60 Evaluation of number-theoretic constants
11A55 Continued fractions
41A25 Rate of convergence, degree of approximation

Keywords:

Glaisher-Kinkelin’s constant; Bendersky-Adamchik’s constants; continued fraction; rate of convergence; asymptotic expansion
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Full Text: DOI

References:

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