Continued fraction approximations to the temperature integral

Abstract

The simplest phenomenological model describing thermoluminescence becomes the one-trap-one recombination center model (OTOR). As it is known, the analysis of thermoluminescence data greatly benefits from separation of a glow curve into separate glow peaks. The shape of the peaks in thermoluminescence dosimetry can be represented by the so-called temperature integral. The highly important and close relation between the complementary incomplete gamma function $\Gamma(a,z)$ and the temperature integral in thermoluminescence dosimetry has engaged specialists to pursue a more accurate calculation of $\Gamma(a,z)$. In this work, new approximations for the temperature integral, considering the fast convergence of continued fractions and the straightforward evaluation of the algebraic expressions are obtained. The new reported approximants improve the calculation efficiency of the temperature integral. The simplicity or precision of resent approximations, have a strong effect on values of physical quantities obtained from thermoluminescence data.