C323: Fermi-Dirac Function

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 15.05.1987
Language: Fortran	Revised: 01.12.1994

Function subprograms RFERDR and DFERDR calculate the Fermi-Dirac function

for real argument x, and k=-1,1,3.

On CDC and Cray computers, the double-precision version DFERDR is not available.

Structure:

FUNCTION subprograms
User Entry Names: RFERDR, DFERDR
Obsolete User Entry Names: FERDR RFERDR
External References: MTLMTR, ABEND

Usage:

In any arithmetic expression,

RFERDR(X,K) or DFERDR(X,K) has the value ,

where RFERDR is of type REAL, DFERDR is of type DOUBLE PRECISION, and X has the same type as the function name. K (INTEGER) = -1, or 1 or 3.

Method:

Rational approximation.

Accuracy:

RFERDR (except on CDC and Cray computers) has full single-precision accuracy. For most values of the argument X, DFERDR (and RFERDR on CDC and Cray computers) has, for , an accuracy of 7-10 digits and for , an accuracy of 10 to 14 digits.

Error handling:

Error C323.1: The function value is set equal to zero, and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

1. W.J. Cody and H.C. Thacher,Jr., Rational approximations for Fermi-Dirac integrals of order -1/2, 1/2 and 3/2, Math. Comp. 21 (1967) 30-40.