A theoretical method for obtaining Pad, type approximation to temperature integrals via the Stieltjes integral

摘要

The normal and generalized temperature integrals originate from the use of the Arrhenius and Harcourt-Esson equations in non-isothermal chemical kinetics analysis of solid materials, where approximate expressions to them are to be required. The aim of the present theoretical exploration is to provide both useful formulas and new insights to this problem; to the end, we address this with an extended view and new method. First, we derive an analytical connection between the two temperature integrals in terms of the Stieltjes integral. Secondly, based on this finding, a unified approach to obtaining approximate expressions of them is developed, which makes use of mathematical relationships between the Stieltjes integral, Stieltjes series and Pad, approximant and leads to new Pad, type approximations to the two integrals. Lastly, an error analysis and comparison of the proposed approximations along with published ones is performed, showing that they are accurate enough and applicable in thermal analysis.