The Stieltjes constants, their relation to the eta_j coefficients, and representation of the Hurwitz zeta function
| dc.creator | Coffey, Mark W. | |
| dc.date | 2007-06-03 | |
| dc.date | 2009-02-25 | |
| dc.date.accessioned | 2026-07-07T12:45:59Z | |
| dc.date.available | 2026-07-07T12:45:59Z | |
| dc.description | The Stieltjes constants gamma_k(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about its only pole at s=1. We present the relation of gamma_k(1) to the eta_j coefficients that appear in the Laurent expansion of the logarithmic derivative of the Riemann zeta function about its pole at s=1. We obtain novel integral representations of the Stieltjes constants and new decompositions such as S_2(n) = S_gamma(n) + S_Lambda(n) for the crucial oscillatory subsum of the Li criterion for the Riemann hypothesis. The sum S_γ(n) is O(n) and we present various integral representations for it. We present novel series representations of S_2(n). We additionally present a rapidly convergent expression for γ_k= γ_k(1) and a variety of results pertinent to a parameterized representation of the Riemann and Hurwitz zeta functions. | |
| dc.description | 37 pages, no figures Prop. 3(b) added and minor updates | |
| dc.identifier | https://arxiv.org/abs/0706.0343 | |
| dc.identifier | http://arxiv.org/abs/0706.0343 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221231 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 11M06, 11M35, 33B15 | |
| dc.title | The Stieltjes constants, their relation to the eta_j coefficients, and representation of the Hurwitz zeta function | |
| dc.type | text |