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  • Author or Editor: M. Balarin x
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The exponential integral in non-isothermal kinetic equations for tempering with linear heating can be represented in the following analytical form
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\int\limits_0^T {e^{ - E/kT'} dT'} = \frac{{kT^2 /E}}{{\sqrt {1 + 4kT/E} }}e^{ - E/kT} ,$$ \end{document}
which is one order inkT/E≪1 more accurate than two other representations recently proposed in this journal [1, 2]. A few variants of approximated forms for the exponential integral are compared with regard to the error due to the kind of approximation, which appears when activation energies are evaluated from experimental non-isothermal kinetic curves.
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