Parameterized summation relations for the Stieltjes constants

Details Parameterized summation relations for the Stieltjes constants Parameterized summation relations for the Stieltjes constants

2010-02-25

arxiv.org/abs/1002.4684v2

Physics

Mathematical Physics

15 pages, no figures, 2 new Propositions, Corollaries, and references added

Scientific paper

The Stieltjes constants $\gamma_k(a)$ appear in the regular part of the Laurent expansion of the Hurwitz zeta function about its only polar singularity at $s=1$. We present multi-parameter summation relations for these constants that result from identities for the Hurwitz zeta function. We also present multi-parameter summation relations for functions $A_k(x)$ that may be expressed as sums over the Stieltjes constants. Integral representations, especially including Mellin transforms, play an important role. As a byproduct, reciprocity and other summatory relations for polygamma functions and Bernoulli polynomials may be obtained.

Affiliated with

Also associated with

No associations

Rating

Parameterized summation relations for the Stieltjes constants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Parameterized summation relations for the Stieltjes constants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Parameterized summation relations for the Stieltjes constants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-379294