Rational approximations of the integral of the Arrhenius function

TLDR: Rational approximations have been derived for the integral of the Arrhenius function dT which is important in the kinetic analysis of thermogravimetric data and is found to be equivalent to the Gorbachev approximation.

Abstract: Rational approximations have been derived for the integral of the Arrhenius function $$\int\limits_0^T {\exp ( - E/RT)}$$ dT which is important in the kinetic analysis of thermogravimetric data. The first degree rational approximation is found to be equivalent to the Gorbachev approximation, i.e., RT2 exp (−E/RT)/(E+2RT). The second degree rational approximation is more accurate than the Zsako empirical approximation when E/RT 5. The third and higher degree rational approximations are found to be more accurate than any other previous approximation.