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The objective of this paper is to provide an efficient and reliable analytical expression for the Einstein integrals using the binomial expansion theorem and power series. The obtained analytical expressions are valid for all values of their arguments. The algorithm can be used in the software and simulation programs. Furthermore, the comparison of the method with numerical calculations shows the applicability and accuracy of the method.

ANALYTICAL EVALUATION OF THE EINSTEIN INTEGRATE USING BINOMIAL EXPANSION THEOREM AND POWER SERIES