Rational Chebyshev approximations for Fermi-Dirac integrals of orders , and

Authors:
W. J. Cody and Henry C. Thacher, Jr.

Journal:
Math. Comp. **21** (1967), 30-40

DOI:
https://doi.org/10.1090/S0025-5718-67-99899-7

Corrigendum:
Math. Comp. **21** (1967), 525.

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Abstract | References | Additional Information

Abstract: Rational Chebyshev approximations are given for the complete Fermi-Dirac integrals of orders and . Maximal relative errors vary with the function and interval considered, but generally range down to or less.

**[1]**A. C. Beer, M. N. Chase & P. F. Choquard, "Extension of McDougall-Stoner tables of the Fermi-Dirac functions,"*Helv. Phys. Acta*, v. 28, 1955, pp. 529-542. MR**17**, 672. MR**0074948 (17:672b)****[2]**G. A. Chisnall, "New tables of Fermi-Dirac functions,"*Jodrell Bank Annals*, v. 1, 1956, pp. 126-140.**[3]**W. J. Cody & J. Stoer, "Rational Chebyshev approximations using interpolation."**[4]**R. B. Dingle, "The Fermi-Dirac integrals ,"*Appl. Sci. Res. Ser.*B, v. 6, 1957, pp. 225-239. MR**19**, 133. MR**0086149 (19:133d)****[5]**R. B. Dingle, "Asymptotic expansions and converging factors. I: General theory and basic converging factors,"*Proc. Roy. Soc. London Ser.*A, v. 244, 1958, pp. 456-475. MR**21**#2145. MR**0103373 (21:2145)****[6]**R. B. Dingle, "Asymptotic expansions and converging factors. III: Gamma, psi and polygamma functions, and Fermi-Dirac and Bose-Einstein integrals,"*Proc. Roy. Soc. London Ser.*A, v. 244, 1958, pp. 484-490. MR**21**#2147. MR**0103375 (21:2147)****[7]**W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions,"*Comm. ACM*, v. 5, 1962, pp. 401-403.**[8]**P. Henrici, "The quotient-difference algorithm,"*Nat. Bur. Standards Appl. Math. Ser.*, No. 49, 1958, pp. 23-46. MR**20**#1410. MR**0094901 (20:1410)****[9]**J. McDougall & E. C. Stoner, "The computation of Fermi-Dirac functions,"*Philos. Trans. Roy. Soc. London Ser.*A, v. 237, 1939, pp. 67-104.**[10]**A. Ralston & H. Wilf,*Mathematical Methods for Digital Computers*, Vol. 2. (To appear.) MR**0117906 (22:8680)****[11]**J. R. Rice, "On the Walsh Arrays for and Erfc ,"*Math. Comp.*, v. 18, 1964, pp. 617-626. MR**29**#6233. MR**0168978 (29:6233)****[12]**H. Werner & G. Raymann, "An Approximation to the Fermi Integral ,"*Math. Comp.*, v. 17, 1963, pp. 193-194. MR**28**#1328. MR**0158102 (28:1328)**

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-67-99899-7

Article copyright:
© Copyright 1967
American Mathematical Society