A new general procedure developed here improves the calculation of both Laplace-type integrals and convergent power series: integral(infinity)(0) t(alpha)exp(-xt)F(t)dt and Sigma(infinity)(n=1)a(n)chi(n) Integrals and series of this type (which often depend on parameters) arise frequently in the solution of important chemical engineering problems, especially in the transport and chemical reaction areas. The results of this study yield convenient analytical approximations. A recursive algorithm determines the required numerical coefficients with the aid of a computer. Several examples illustrate the features of the new technique. Some comparisons are made to earlier improvement methods, such as Pade approximation.