论文标题
1D和2D中的修改后的Euler-Maclaurin公式，并在统计物理中应用
A modified Euler-Maclaurin formula in 1D and 2D with applications in statistical physics
论文作者
论文摘要
Euler-Maclaurin求和公式通过将周期性的Bernoulli多项式作为其傅立叶序列并进行切割，将其推广到修改形式，其中包括Euler-Maclaurin求和公式和Poission Sumpation求和公式作为特殊情况。通过使用修改公式，获得了数值求和方法，并可以控制误差。修改的公式也从一个维度概括为两个布置。还讨论了其在统计物理学中的应用示例。
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.
