C323 Fermi-Dirac Function

Function subprograms RFERDR and DFERDR calculate the Fermi-Dirac function

$F$_k(x) = ∫₀^&inf;{t^k/21+e^t-x} dt

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 $\equiv$ RFERDR
External References: MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, RFERDR(X,K) or DFERDR(X,K) has the value $F$_K(X) ,

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 $X>0$ , an accuracy of 7-10 digits and for , an accuracy of 10 to 14 digits.

Error handling:

Error C323.1: $K\; \ne -1,1,3.$

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.

C324