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

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, and P. F. Choquard,*Extension of McDougall-Stoner tables of the Fermi-Dirac functions*, Helv. Phys. Acta**28**(1955), 529–542. MR**0074948****[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 ℱ_{𝓅}(𝜂)=(𝓅!)⁻¹∫^{∞}₀𝜀^{𝓅}(ℯ^{𝜀-𝜂}+1)⁻¹𝒹𝜀*, Appl. Sci. Res. B.**6**(1957), 225–239. MR**0086149****[5]**R. B. Dingle,*Asymptotic expansions and converging factors. I. General theory and basic converging factors*, Proc. Roy. Soc. London. Ser. A**244**(1958), 456–475. MR**0103373****[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**244**(1958), 484–490. MR**0103375****[7]**W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions,"*Comm. ACM*, v. 5, 1962, pp. 401-403.**[8]**Peter Henrici,*The quotient-difference algorithm*, Nat. Bur. Standards Appl. Math. Ser. no.**49**(1958), 23–46. MR**0094901****[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]***Mathematical methods for digital computers*, John Wiley & Sons, Inc., New York-London, 1960. MR**0117906****[11]**John R. Rice,*On the 𝐿_{∞} Walsh arrays for Γ(𝑥) and 𝐸𝑟𝑓𝑐(𝑥)*, Math. Comp.**18**(1964), 617–626. MR**0168978**, 10.1090/S0025-5718-1964-0168978-8**[12]**H. Werner and G. Raymann,*An approximation to the Fermi integral 𝐹_{1\over2}(𝑥)*, Math. Comp.**17**(1963), 193–194. MR**0158102**, 10.1090/S0025-5718-1963-0158102-9

Additional Information

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

Article copyright:
© Copyright 1967
American Mathematical Society