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There is no standard procedure for calculating the generalized temperature integral, instead myriads of different approximations to it are applied in the processing of thermogravimetric analysis data. This work presents an integration procedure based on the Simpson rule that generates exact values of the generalized temperature integral. It also reviews the available representations of the temperature integral in power series, and presents the conversion of its generalized form into the form of special functions. From the comparison with the exact values from integration it was concluded that for argument values of practical interest the generalized temperature integral is best computed as the incomplete gamma function.

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