I have finished some further work on the Exponential Integrals and attached the
files to the feature request on Sourceforge.net.
The following features are now implemented:
1. Numerical evaluation for complex Flonum and Bigfloat numbers
using an expansion in a power series or continued fractions.
The numerical support is fully implemented for the E[n](z) function.
All other functions call E[n](z) for numerical evaluation.
Because we have no support for a Gamma function with complex Bigfloat
arguments, the numerical evaluation for complex parameters n is not
implemented for Complex Bigfloats.
2. For a negative integer parameter E[n](z) is automatically expanded in
a finite series in terms of powers and the Exponential function.
3. When $expintexpand is set to TRUE or ERF E[n](z) expands
a) for n a half integral number in terms of Erfc (TRUE) or Erf (ERF)
b) for n a positive integer number in terms of Ei
3. Simplifications for special values: Ev(0), E[0](z), Li(0), Li(1),...
4. Derivatives of the Exponential Integrals
5. Change the representation of every Exponential Integral through other
Exponential Integrals or the Gammaincomplete function.
Implementing the Exponential Integrals I have found the following things which
could be done also:
1. Gamma function with support for Complex Bigfloats
2. More support for the Erf and Erfc functions
3. More support for the Gammaincomplete function
4. More correct simplification of the Log function
Dieter Kaiser