Addison-type series representation for the Stieltjes constants

作者：Coffey Mark W^*

来源：Journal of Number Theory, 2010, 130(9): 2049-2064.

DOI：10.1016/j.jnt.2010.01.003

• Stieltjes constants
• Riemann zeta function
• Laurent expansion
• Series representation
• Hurwitz zeta function

The Stieltjes constants gamma(k)(a) appear in the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function zeta(s, a) about its only pole at s = 1. We generalize a technique of Addison for the Euler constant gamma = gamma(0)(1) to show its application to finding series representations for these constants. Other generalizations of representations of gamma are given.

• 出版日期2010-9