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ISSN 1088-6842(e) ISSN 0025-5718(p)

An effective asymptotic formula for the Stieltjes constants

Author(s): Charles Knessl; Mark W. Coffey.
Journal: Math. Comp. 80 (2011), 379-386.
MSC (2010): Primary 41A60, 30E15, 11M06
Posted: June 9, 2010
MathSciNet review: 2728984
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Abstract | References | Similar articles | Additional information

Abstract: The Stieltjes constants $\gamma_k$ appear in the coefficients in the regular part of the Laurent expansion of the Riemann zeta function $\zeta(s)$ about its only pole at . We present an asymptotic expression for $\gamma_k$ for $k \gg 1$ . This form encapsulates both the leading rate of growth and the oscillations with . Furthermore, our result is effective for computation, consistently in close agreement (for both magnitude and sign) for even moderate values of . Comparison to some earlier work is made.

References:

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Additional Information:

Charles Knessl
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045

Mark W. Coffey
Affiliation: Department of Physics, Colorado School of Mines, Golden, Colorado 80401

DOI: 10.1090/S0025-5718-2010-02390-7
PII: S 0025-5718(2010)02390-7
Keywords: Stieltjes constants, Riemann zeta function, Laurent expansion,
Received by editor(s): September 25, 2009
Received by editor(s) in revised form: November 2, 2009
Posted: June 9, 2010
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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