The Stieltjes function--definition and properties

Authors:
Jan Bohman and Carl-Erik Fröberg

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

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Abstract: Close to the singular point the zeta function can be represented as a Laurent series in . 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.

**[1]**J. L. W. V. Jensen, "Sur la fonction de Riemann,"*C. R. Acad. Sci. Paris*, v. 104, 1887, pp. 1156-1159.**[2]**J. P. Gram, "Note sur le calcul de la fonction de Riemann,"*Det Kgl. Danske Vid. Selsk. Overs.*, 1895, pp. 303-308.**[3]**J. J. Y. Liang & John Todd, "The Stieltjes constants,"*J. Res. Nat. Bur. Standards Sect. B.*, v. 76B, 1972, pp. 161-178. MR**0326974 (48:5316)****[4]**T. M. Apostol, "Formulas for higher derivatives of the Riemann zeta function,"*Math. Comp.*, v. 44, 1985, pp. 223-232. MR**771044 (86c:11063)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0942155-9

Article copyright:
© Copyright 1988
American Mathematical Society