Table 1 Comparison of approximation formulas (5.1)–(5.4)
From: Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^{n}\)
n | \(\frac{u_{n}-V_{n}}{V_{n}}\) | \(\frac{V_{n}-v_{n}}{V_{n}}\) | \(\frac{w_{n}-V_{n}}{V_{n}}\) | \(\frac{r_{n}-V_{n}}{V_{n}}\) |
|---|---|---|---|---|
10 | 2.2651 × 10−3 | 1.885 × 10−3 | 9.3351 × 10−5 | 1.1467 × 10−8 |
100 | 2.4751 × 10−5 | 1.885 × 10−5 | 1.2131 × 10−7 | 2.1845 × 10−15 |
1000 | 2.4975 × 10−7 | 2.4925 × 10−7 | 1.2462 × 10−10 | 2.3273 × 10−22 |
10,000 | 2.4997 × 10−9 | 2.4992 × 10−9 | 1.2496 × 10−13 | 2.3421 × 10−29 |