Table 1 Comparison among \(W_{02}\) (1.9), \(W_{L2}\) (5.3), \(W_{1}\) (1.3), \(W_{01}^{\ast }\) (1.10) and \(W_{L1}\) (5.2)
From: Windschitl type approximation formulas for the gamma function
n | \(\vert \frac{W_{02} ( n ) -n!}{n!} \vert \) | \(\vert \frac{W_{L2} ( n ) -n!}{n!} \vert \) | \(\vert \frac{W_{1} ( x ) -n!}{n!} \vert \) | \(\vert \frac{W_{01}^{\ast } ( x ) -n!}{n!} \vert \) | \(\vert \frac{W_{L1} ( x ) -n!}{n!} \vert \) |
|---|---|---|---|---|---|
1 | 3.065 × 10−4 | 5.655 × 10−4 | 1.832 × 10−4 | 2.754 × 10−4 | 4.686 × 10−4 |
2 | 1.098 × 10−6 | 1.629 × 10−6 | 2.668 × 10−6 | 3.449 × 10−6 | 5.030 × 10−6 |
5 | 3.956 × 10−10 | 5.367 × 10−10 | 5.743 × 10−9 | 7.054 × 10−9 | 9.681 × 10−9 |
10 | 8.221 × 10−13 | 1.098 × 10−12 | 4.710 × 10−11 | 5.738 × 10−11 | 7.794 × 10−11 |
20 | 1.630 × 10−15 | 2.172 × 10−15 | 3.727 × 10−13 | 4.531 × 10−13 | 6.138 × 10−13 |
50 | 4.300 × 10−19 | 5.715 × 10−19 | 6.129 × 10−16 | 7.445 × 10−16 | 1.008 × 10−15 |
100 | 8.404 × 10−22 | 1.117 × 10−21 | 4.791 × 10−18 | 5.819 × 10−18 | 7.877 × 10−18 |