expn

Exponential integral En.

SYNOPSIS:

int n;
double x, y, expn();
y = expn(n, x);

DESCRIPTION:

Evaluates the exponential integral.

                 inf.
                   -
                  | |   -xt
                  |    e
      E (x) =    |    ---- dt.
       n          |      n
                | |     t
                 -
                  1

Both n and x must be nonnegative.

The routine employs either a power series, a continued fraction, or an asymptotic formula depending on the relative values of n and x.

ACCURACY:
                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC       0, 30        5000       2.0e-16     4.6e-17
    IEEE      0, 30       10000       1.7e-15     3.6e-16