2 research outputs found
Arbitrary-precision computation of the gamma function
We discuss the best methods available for computing the gamma function in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function , the digamma function , and derivatives and . Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results