C339 Dawson's Integral

Function subprograms RDAWSN and DDAWSN calculate the Dawson integral

$F(x)\; =\; e-x2\int$₀^xe^t2dt

for real arguments x.

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

Structure:

FUNCTION subprograms
User Entry Names: RDAWSN, DDAWSN
Obsolete User Entry Names: DAWSON $\equiv$ RDAWSN

Usage:

In any arithmetic expression, RDAWSN(X) or DDAWSN(X) has the value $F(X)$ ,

where RDAWSN is of type REAL, DDAWSN is of type DOUBLE PRECISION, and X has the same type as the function name.

Method:

Rational approximation.

Accuracy:

RDAWSN (except on CDC and Cray computers) has full single-precision accuracy. For most values of the argument X, DDAWSN (and RDAWSN on CDC and Cray computers) has an accuracy of approximately one significant digit less than the machine precision.

References:

1. W.J. Cody, K.A. Paciorek and H.C. Thacher,Jr., Chebyshev approximations for Dawson's integral, Math. Comp. 24 (1970) 171--178.

C340