Abstract
The exponential integral\(p(x) = - \int\limits_\infty ^x {\frac{{e^{ - u} }}{{u^2 }}} \cdot du\) can be approximated by means of the empirical formula\(p(x) \approx \frac{{e^{ - x} }}{{(x - d)(x + 2)}}\) with\(d = \frac{{16}}{{(x^2 - 4x + 84)}}\). Ifx> 1.6, errors are less than 0.5%.
References
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Handbook of Mathematical Functions, Edited byM. Obranowitz andI. A. Stegun, Dover Publ. Inc. New York, 1965, p. 238.
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Zsakó, J. Empirical formula for the exponential integral in non-isothermal kinetics. Journal of Thermal Analysis 8, 593–596 (1975). https://doi.org/10.1007/BF01910139
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DOI: https://doi.org/10.1007/BF01910139