Fast computation of the Stieltjes constants
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- by José A. Adell and Alberto Lekuona PDF
- Math. Comp. 86 (2017), 2479-2492 Request permission
Abstract:
We evaluate each Stieltjes constant $\gamma _m$ as a finite sum involving the first $m+1$ Bernoulli numbers $B_k$ and the first $m+1$ derivatives $(-1)^k\alpha _k$ of the alternating zeta function at the point 1. In turn, we compute each $\alpha _k$ in an efficient way by means of a series with geometric rate 1/3. The coefficients of such a series are bounded and slowly decrease to zero. The computational significance of the preceding results is also discussed.References
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Additional Information
- José A. Adell
- Affiliation: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
- MR Author ID: 340766
- Email: adell@unizar.es
- Alberto Lekuona
- Affiliation: Departamento de Métodos Estadísticos, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
- MR Author ID: 663604
- Email: lekuona@unizar.es
- Received by editor(s): April 21, 2015
- Received by editor(s) in revised form: December 22, 2015, and April 26, 2016
- Published electronically: March 3, 2017
- Additional Notes: The authors were partially supported by Research Projects MTM2011-23998 and DGA, E-64, and by FEDER funds.
- © Copyright 2017 American Mathematical Society
- Journal: Math. Comp. 86 (2017), 2479-2492
- MSC (2010): Primary 11M06; Secondary 60G51
- DOI: https://doi.org/10.1090/mcom/3176
- MathSciNet review: 3647968