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


Authors: Edward W. Ng, C. J. Devine and R. F. Tooper
Journal: Math. Comp. 23 (1969), 639-643
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1969-0247739-X
MathSciNet review: 0247739
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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}}$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0247739-X
Article copyright: © Copyright 1969 American Mathematical Society

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