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An Effective Asymptotic Formula for the Stieltjes Constants

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Title: An Effective Asymptotic Formula for the Stieltjes Constants
Author(s): Knessl, Charles; Coffey, Mark W.
Subject(s): Stieltjes asymptotic
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 s = 1. We present an asymptotic expression for gamma(k) for k >> 1. This form encapsulates both the leading rate of growth and the oscillations with k. Furthermore, our result is effective for computation, consistently in close agreement (for both magnitude and sign) for even moderate values of k. Comparison to some earlier work is made.
Issue Date: 2011-01
Publisher: American Mathematical Society
Citation Info: Knessl, C. & Coffey, M. W. 2011. An Effective Asymptotic Formula for the Stieltjes Constants. Mathematics of Computation, 80(273): 379-386. DOI: 10.1090/S0025-5718-2010-02390-7.
Type: Article
Description: First published in Mathematics of Computation in 2011; published by the American Mathematical Society; DOI: 10.1090/S0025-5718-2010-02390-7
URI: http://hdl.handle.net/10027/7712
ISSN: 0025-5718
Date Available in INDIGO: 2011-05-27
 

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