Table 1 Simulations for \(\pmb{\alpha_{1}(n)}\) , \(\pmb{\alpha_{2}(n)}\) and \(\pmb{\beta (n)}\)
From: Approximation for the gamma function via the tri-gamma function
n | \(\boldsymbol{\frac{\alpha _{1}(n)-n!}{n!}}\) | \(\boldsymbol{\frac{\alpha _{2}(n)-n!}{n!}}\) | \(\boldsymbol{\frac{\beta (n)-n!}{n!}}\) |
|---|---|---|---|
50 | 9.7924 × 10−19 | 1.1997 × 10−24 | −7.0866 × 10−28 |
500 | 9.8013 × 10−28 | 1.2019 × 10−37 | −7.1217 × 10−43 |
1000 | 1.9143 × 10−30 | 1.4672 × 10−41 | −2.1734 × 10−47 |
2000 | 3.7389 × 10−33 | 1.7910 × 10−45 | −6.63 × 10−52 |