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