Chebyshev polynomial expansion of BoseEinstein functions of orders to
Authors:
Edward W. Ng, C. J. Devine and R. F. Tooper
Journal:
Math. Comp. 23 (1969), 639643
MSC:
Primary 65.25
MathSciNet review:
0247739
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Abstract: Chebyshev series approximations are given for the complete BoseEinstein 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 FermiDirac 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
(21 #4264)
 [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
(6,152a)
 [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
(9,431a)
 [5]
R. B. Dingle, "The BoseEinstein integrals," Appl. Sci. Res. B, v. 6, 1957, pp. 240244. 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
(29 #4914)
 [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, SpringerVerlag New York, Inc., New
York, 1966. MR
0232968 (38 #1291)
 [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 (16,523c)
 [1]
 L. Lewin, Dilogarithms and Associated Functions, MacDonald, London, 1958. MR 21 #4264. MR 0105524 (21:4264)
 [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., v. 46, 1945, p. 144. MR 0011344 (6:152a)
 [4]
 C. Truesdell, A Unified Theory of Special Functions, Ann. of Math. Studies, no. 18, Princeton Univ. Press, Princeton, N. J., 1948. MR 9, 431. MR 0023960 (9:431a)
 [5]
 R. B. Dingle, "The BoseEinstein integrals," Appl. Sci. Res. B, v. 6, 1957, pp. 240244. MR 19, 133.
 [6]
 K. S. Kölbig, "Algorithm 327: Dilogarithm," Comm. Assoc. Comput. Mach., v. 11, 1968, p. 270.
 [7]
 M. Abramowitz & I. A. Stegun, (Editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Nat. Bur. Standards Appl. Math. Series, No. 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964; 3rd printing with corrections, 1965. MR 29 #4914; MR 31 #1400. MR 0167642 (29:4914)
 [8]
 W. Magnus, F. Oberhettinger & R. Soni, Special Functions of Mathematical Physics, SpringerVerlag, New York, 1966. MR 0232968 (38:1291)
 [9]
 C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Lab. Math. Tables, vol. 5, HMSO, London, 1962. MR 26 #362.
 [10]
 Staff of the Computation Department, Mathematisch Centrum, Amsterdam, Table of Polylogarithms, Part I: Numerical Values, Report R24, 1954. See MTAC, v. 9, 1955, p. 40, RMT 29. MR 16, 523. MR 0066028 (16:523c)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819690247739X
PII:
S 00255718(1969)0247739X
Article copyright:
© Copyright 1969
American Mathematical Society
