A note on the approximation of the incomplete gamma function by a method of G. Meinardus (Q1094561)

The paper gives the details on the construction by a method of Meinardus of a near-best approximation to the function \(z(s,x)=e^ xx^{1- s}\Gamma (s,x)\), where \(\Gamma\) (s,x) is the incomplete gamma function. This approximation can be viewed as an alternative for the well-known asymptotic expansion of z(s,x) as \(x\to \infty\). The note gives several possibilities for the numerical computation of the coefficients in the approximating polynomial. It would be interesting to compare this approach with other useful methods, for instance with the continued fraction. The reference to the paper of Meinardus contains an error. It appeared in Comput. Math. Appl., Part B 12, 1191-1201 (1986; Zbl 0631.33002).