Table 1 Comparison among approximation formulas ( 5.6 )-( 5.8 )
From: Padé approximant related to asymptotics for the gamma function
n | \(\boldsymbol {\frac{\lambda_{n}-n!}{n!}}\) | \(\boldsymbol {\frac{U_{n}-n!}{n!}}\) | \(\boldsymbol {\frac{n!-V_{n}}{n!}}\) |
|---|---|---|---|
10 | 1.7686 × 10−9 | 3.6355 × 10−11 | 3.5843 × 10−13 |
100 | 1.7855 × 10−14 | 3.7108 × 10−18 | 3.7317 × 10−22 |
1,000 | 1.7857 × 10−19 | 3.7115 × 10−25 | 3.7332 × 10−31 |
10,000 | 1.7857 × 10−24 | 3.7115 × 10−32 | 3.7333 × 10−40 |