C324 Arctangent integral

Function subprograms RATANI and DATANI calculate the arctangent integral

$Ti$₂(x) = ∫₀^x{arctantt} dt

for real argument x.

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

Structure:

FUNCTION subprograms
User Entry Names: RATANI, DATANI
Obsolete User Entry Names: ATANI $\equiv$ RATANI

Usage:

In any arithmetic expression, RATANI(X) or DATANI(X) has the value $Ti$₂(X) ,

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

Method:

Approximation by truncated Chebyshev series and functional relations.

Accuracy:

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

References:

1. Y.L. Luke, Mathematical functions and their approximations, (Academic Press New York, 1975) 67.

C326