论文标题
具有复杂系数的$γ$功能的Lanczos近似
The Lanczos Approximation for the $Γ$-Function with Complex Coefficients
论文作者
论文摘要
我们检查了\ cite {lanczos1964}的系数的属性，当使用这些系数时，$γ$函数具有带有自由参数的复杂值，以及近似值的收敛性。我们报告说，对于固定的自由参数的真实部分，使用复杂系数都会增加兰开斯近似的计算成本，同时引起精度。我们得出的结论是，在对$γ$函数的数值评估的实际应用中，仅应使用具有自由参数的实际值生成的系数。
We examined the properties of the coefficients of the \cite{lanczos1964} approximation of the $Γ$-function with complex values of the free parameter together with the convergence properties of the approximation when using these coefficients. We report that for fixed real parts of the free parameter that using complex coefficients both increases the computational cost of the Lanczos approximation while drecreasing the accuracy. We conclude that in practical applications of numerical evaluation of the $Γ$-function only coefficients generated with real values of the free parameter should be used.
