Algorithm 779: Fermi-Dirac Functions of Order -1/2, 1/2, 3/2, 5/2

ACM Transactions on Mathematical Software

Volumn 24, Issue 1, 1998, Pages 1-12

  Macleod, Allan J ^a  

^a UNIVERSITY OF THE WEST OF SCOTLAND   (United Kingdom)

Author keywords

Algorithms; Chebyshev polynomials; Collocation; D.3.2 Programming Languages : Language Classifications Fortran 77; F.2.1 Analysis of Algorithms and Problem Complexity : Numerical Algorithms and Problems; G.1.2 Numerical Analysis : Approximation

Indexed keywords

ALGORITHMS; CHEBYSHEV APPROXIMATION; DIGITAL ARITHMETIC; POLYNOMIALS;

CHEBYSHEV POLYNOMIAL EXPANSIONS; FERMI-DIRAC FUNCTIONS; PRECISION;

NATURAL SCIENCES COMPUTING;

EID: 0032010653     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/285861.285862     Document Type: Article

References (20)

1. ABRAMOWITZ, M. AND STEGUN, I. A., EDS. 1964. Handbook of Mathematical Functions. Dover Publications, Inc., Mineola, NY.
2. BANUELOS, A., DEPINE, R. A., AND MANCINI, R. C. 1981. A program for computing the Fermi-Dirac functions. Comput. Phys. Commun. 21, 315-322.
3. BLAKEMORE, J. S. 1987. Semiconductor Statistics. Dover Publications, Inc., Mineola, NY.
4. BRENT, R. P. 1978. A Fortran multiple precision arithmetic package. ACM Trans. Math. Softw. 4, 1 (Mar.), 57-70.
5. CLENSHAW, C. W. 1957. The numerical solution of linear differential equations in Chebyshev series. Camb. Phil. Soc. Math. Proc. 53, 134-149.
6. CODY, W. J. 1988. Algorithm 665: MACHAR: A subroutine to dynamically determine machine parameters. ACM Trans. Math. Softw. 14, 4 (Dec.), 303-311.
7. CODY, W. J. AND THACHER, H. C. 1967. Rational Chebyshev approximations for Fermi-Dirac integrals of orders -1/2, 1/2, and 3/2. Math. Comput. 21, 30-40.
8. FULLERTON, L. W. 1976. Portable special function routines. In Portability of Numerical Software, W. Cowell, Ed. Springer Lecture Notes in Computer Science, vol. 57. Springer-Verlag, New York, NY, 452-483.
9. FULLERTON, L. W. AND RINKER, G. A. 1986. Generalised Fermi-Dirac integrals - FD, FDG, FDH. Comput. Phys. Commun. 39, 181-185.
10. j(x) over the entire domain of real j and x. Solid-State Elec. 36, 217-221.
11. GOANO, M. 1995. Algorithm 745: Computation of the complete and incomplete Fermi-Dirac integral. ACM Trans. Math. Softw. 21, 3 (Sept.), 221-232.
12. HART, J. F., CHENEY, E. W., LAWSON, C. L., MAEHLY, H. J., MESZTENYI, C. K., RICE, J. R., THACHER, H. G., AND WITZGALL, C. 1968. Computer Approximations. John Wiley & Sons, Inc., New York, NY.
13. LOZIER, D. W. AND OLVER, F. W. J. 1995. Numerical evaluation of special functions. In Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics, W. Gautschi, Ed. Proceedings of Symposia in Applied Mathematics, vol. 48. American Mathematical Society, Boston, MA, 79-126.
14. MACLEOD, A. J. 1993. Chebyshev expansions for modified Struve and related functions. Math. Comput. 60, 735-747.
15. MCDOUGALL, J. AND STONER, E. C. 1938. The computation of Fermi-Dirac functions. Phil. Trans. Roy. Soc. London 237, 67-104.
16. OLIVER, J. 1977. An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. IMA 20, 379-391.
17. SCHONFELDER, J. L. 1976. The production of special function routines for a multi-machine library. Softw. Pract. Exper. 6, 71-82.
18. SMITH, D. A. AND FORD, W. F. 1979. Acceleration of linear and logarithmic convergence. SIAM J. Numer. Anal. 16, 223-240.
19. WIMP, J. 1984. Computation with Recurrence Relations. Pitman Publishing, Inc., Marshfield, MA.
20. WONG, S. A., MCALISTER, S. P., AND LI, Z.-M. 1994. A comparison of some approximations for the Fermi-Dirac integral of order 1/2. Solid-State Elec. 37, 61-64.