Chebyshev polynomial expansion of Bose-Einstein functions of orders $1$ to $10$

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 $2 \times {10^{ - 20}}$ to $3 \times {10^{ - 19}}$. These expansions are fast convergent; for example, typically six terms gives an accuracy of ${10^{ - 8}}$.