An approximation of the gamma function
A very good approximation of the gamma function is found. This approximation comes from a trapezoidal rule. The error of the approximation is estimated through a Fourier expansion. All completely monotone solutions of the functional equation \(\phi (ax)=b\phi (x)\) are described. Why any completely monotone solution is close to a power of x is explained with that approximation of the gamma function.
scientific article; zbMATH DE number 4144380