The Stieltjes function—definition and properties
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- by Jan Bohman and Carl-Erik Fröberg PDF
- Math. Comp. 51 (1988), 281-289 Request permission
Abstract:
Close to the singular point $s = 1$ the zeta function can be represented as a Laurent series in $(s - 1)$. The coefficients in this series are called the Stieltjes constants, and the first ones were computed already 100 years ago. In order to investigate their somewhat unexpected behavior we have defined a related function which we call the Stieltjes function, and examined its properties.References
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J. L. W. V. Jensen, "Sur la fonction $\zeta (s)$ de Riemann," C. R. Acad. Sci. Paris, v. 104, 1887, pp. 1156-1159.
J. P. Gram, "Note sur le calcul de la fonction $\zeta (s)$ de Riemann," Det Kgl. Danske Vid. Selsk. Overs., 1895, pp. 303-308.
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 51 (1988), 281-289
- MSC: Primary 11M06; Secondary 11Y35, 33A10, 65B10
- DOI: https://doi.org/10.1090/S0025-5718-1988-0942155-9
- MathSciNet review: 942155