The Lanczos formula for the Gamma function is used in many software libraries due to its favorable convergence properties for complex argument. A simple proof that the formula interpolates the factorial function at the first few integers is given. A new interpolating formula is then proposed, which is more accurate, and attains a nearly uniform relative error.

翻译：用于 Gamma 函数的 Lanczos 公式在许多软件库中使用, 这是因为它对于复杂参数具有有利的趋同特性。 给出了一个简单的证据, 证明公式在最初几个整数中乘以系数函数。 然后提出了一个新的内插公式, 这个公式更准确, 并得出几乎统一的相对错误 。