Some preliminary observations on an algorithm for the computation of moment integrals (Q1091750)

The authors investigate the computation of Stieltjes moment integrals of the type \(\sigma_ n=\int^{\infty}_{0}t^ ne^{-P(t)} dt,\) \(n=0,1,2,..\). where P(t) is entire, with \(t^{N_ e-P(t)}=O(1)\), \(t\in {\mathbb{R}}\), for all N, and \(P(t)=\sum^{\infty}_{k=1}P_ kt^ k\). For this they introduce a Miller type algorithm: \(\sigma_ n=1/(n+1)\sum^{\infty}_{k=0}(k+1)P_{k+1}\sigma_{n+k+1}\). The relative adjoint algorithm and the convergence of the algorithm are studied and numerical examples are taken into account.