Chebyshev approximations for the psi function

Abstract

Rational Chebyshev approximations to the psi (digamma) function are presented for .5 ≦ x ≦ 3.0 .5 \leqq x \leqq 3.0 , and 3.0 ≦ x 3.0 \leqq x . Maximum relative errors range down to the order of 10 − 20 {10^{ - 20}} .