New rational fraction approximating formulas for the temperature integral

Three rational fraction approximations for the temperature integral have been proposed using the pattern search method. The validity of the new approximations has been tested by some numerical analyses. Compared with several published approximating formulas, the new approximations is more accurate than all approximations except the approximations proposed by Senum and Yang in the range of 5 <= E/RT <= 100. For low values of E/RT, the new approximations are superior to Senum-Yang approximations as solutions of the temperature integral.