Chebyshev polynomial expansion of Bose-Einstein functions of orders to

Authors:
Edward W. Ng, C. J. Devine and R. F. Tooper

Journal:
Math. Comp. **23** (1969), 639-643

MSC:
Primary 65.25

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 to . These expansions are fast convergent; for example, typically six terms gives an accuracy of .

**[1]**L. Lewin,*Dilogarithms and associated functions*, Foreword by J. C. P. Miller, Macdonald, London, 1958. MR**0105524****[2]**R. J. Swenson, "Evaluation of Fermi and Bose integrals,"*Phys. Lett.*, v. 26A, 1968, p. 632.**[3]**C. Truesdell,*On a function which occurs in the theory of the structure of polymers*, Ann. of Math. (2)**46**(1945), 144–157. MR**0011344****[4]**C. Truesdell,*An Essay Toward a Unified Theory of Special Functions Based upon the Functional Equation (∂/∂𝑧)𝐹(𝑧,𝛼)=𝐹(𝑧,𝛼+1)*, Annals of Mathematics Studies, no. 18, Princeton University Press, Princeton, N. J., 1948. MR**0023960****[5]**R. B. Dingle, "The Bose-Einstein integrals,"*Appl. Sci. Res. B*, v. 6, 1957, pp. 240-244. MR**19**, 133.**[6]**K. S. Kölbig, "Algorithm 327: Dilogarithm,"*Comm. Assoc. Comput. Mach.*, v. 11, 1968, p. 270.**[7]**Milton Abramowitz and Irene A. Stegun,*Handbook of mathematical functions with formulas, graphs, and mathematical tables*, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR**0167642****[8]**Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni,*Formulas and theorems for the special functions of mathematical physics*, Third enlarged edition. Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR**0232968****[9]**C. W. Clenshaw,*Chebyshev Series for Mathematical Functions*, National Physical Lab. Math. Tables, vol. 5, HMSO, London, 1962. MR**26**#362.**[10]***Polylogarithms. Part I: Numerical values*, Rekenafdeling. Rep. R24, Math. Centrum Amsterdam., 1954. By the staff of the computation department. MR**0066028**

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DOI:
https://doi.org/10.1090/S0025-5718-1969-0247739-X

Article copyright:
© Copyright 1969
American Mathematical Society