This paper gives an approximation for gamma function that, while different, has the same form as Lanczos one. Both approximations correct Stirling's approximation with contributions from the gamma function's poles a require \(O (-\log \varepsilon)\) time independent of \(z\) to calculate \(z!\) with \(a\) relative error \(\varepsilon\). At comparable accuracies, this approximation requires slightly more computation, but is superior in two ways: its coefficients are given by simple formulas and error estimations can be applied for the gamma function as well as its derivatives. Thus approximations for the digamma and trigamma functions are also given.