English

High precision computation and a new asymptotic formula for the generalized Stieltjes constants

Numerical Analysis 2022-12-21 v2 Numerical Analysis Number Theory

Abstract

We provide an efficient method to evaluate the generalized Stieltjes constants γn(a)\gamma_n(a) numerically to arbitrary accuracy for large nn and nan \gg |a| values. The method uses an integral representation for the constants and evaluates the integral by applying the double exponential (DE) quadrature method near the saddle points of the integrands. Further, we provide a highly accurate asymptotic formula for the generalized Stieltjes constants.

Keywords

Cite

@article{arxiv.2212.07956,
  title  = {High precision computation and a new asymptotic formula for the generalized Stieltjes constants},
  author = {Sandeep Tyagi},
  journal= {arXiv preprint arXiv:2212.07956},
  year   = {2022}
}