Abstract
Chebyshev series approximations are given for the complete Bose-Einstein functions of orders 1 to 10. This paper also gives an exhaustive presentation of the relation of this function to other functions, with the emphasis that some Fermi-Dirac functions and polylogarithms are readily computable from the given approximations. The coefficients are given in 21 significant figures and the maximal relative error for function representation ranges from 2 × 10<sup>-20</sup> to 3 × 10<sup>-19</sup>. These expansions are fast convergent; for example, typically six terms gives an accuracy of 10<sup>-8</sup>.
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