Analytic continuation of harmonic sums: dispersion representation
arXiv:2205.15182 · doi:10.1016/j.nuclphysb.2022.115976
Abstract
We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole expressions of these sums near negative integers. We describe the procedure for the precise numerical evaluations of the corresponding results from the dispersion representation.
arXiv comment12 pages, 3 ancillary files, typos corrected, links to GitHub added, references added
References in corpus (21)
- Harmonic Polylogarithms
- BFKL pomeron in the next-to-leading approximation
- Numerical evaluation of multiple polylogarithms
- Harmonic sums, Mellin transforms and Integrals
- Harmonic Sums and Mellin Transforms up to two-loop Order
- The Multiple Zeta Value Data Mine
- NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
- Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
- The 3-loop QCD calculation of the moments of deep inelastic structure functions
- Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
- Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
- Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5
- Analytic Continuation of Mellin Transforms up to two-loop Order
- The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity
- Iterated Binomial Sums and their Associated Iterated Integrals
- NNLO BFKL Pomeron eigenvalue in N=4 SYM
- Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
- Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation
- Analytic continuation of the Mellin moments of deep inelastic structure functions
- Analytic Continuation of Harmonic Sums
- BFKL pomeron in the next-to-next-to-leading approximation in the planar N=4 SYM theory