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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