A modified Euler–Maclaurin formula in 1D and 2D with applications in statistical physics

Jihong Guo,Yunpeng Liu

Table 2. Approximate values of ${\bar{R}}_{{np}}^{A}$ [defined in equation (28)] with B = 1.

n 3 5 7 9 11 13 15 p 0 7.8 × 10−2 1.5 × 10−2 5.0 × 10−3 2.2 × 10−3 1.2 × 10−3 7.8 × 10−4 5.9 × 10−4 1 1.3 × 10−2 5.4 × 10−4 4.1 × 10−5 4.4 × 10−6 6.0 × 10−7 9.6 × 10−8 1.8 × 10−8 2 5.0 × 10−3 8.3 × 10−5 2.7 × 10−6 1.2 × 10−7 7.1 × 10−9 5.0 × 10−10 4.2 × 10−11 3 2.6 × 10−3 2.3 × 10−5 3.9 × 10−7 9.8 × 10−9 3.2 × 10−10 1.2 × 10−11 5.7 × 10−13 4 1.6 × 10−3 8.6 × 10−6 9.2 × 10−8 1.4 × 10−9 2.9 × 10−11 7.1 × 10−13 2.1 × 10−14