A modified Euler-Maclaurin formula in 1D and 2D with applications in statistical physics
Mathematical Physics
2021-07-07 v1 math.MP
Abstract
The Euler-Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler-Maclaurin summation formula and the Poission summation formula as special cases. By making use of the modified formula, a numerical summation method is obtained and the error can be controlled. The modified formula is also generalized from one dimention to two dimentions. Examples of its applications in statistical physics are also discussed.
Keywords
Cite
@article{arxiv.2004.10441,
title = {A modified Euler-Maclaurin formula in 1D and 2D with applications in statistical physics},
author = {Jihong Guo and Yunpeng Liu},
journal= {arXiv preprint arXiv:2004.10441},
year = {2021}
}
Comments
14 pages, 3 figures, 4 tables