I don't know the answer to this for certain, but (assuming you mean eq.
5.1.53 on page 231 - http://www.math.sfu.ca/~cbm/aands/page_231.htm ) it
looks to me like this might just a 5th degree polynomial interpolation
(in which case, it's of course not something that you can compute to
arbitrary precision without computing E1 to arbitrary precision first).
In particular, the first few terms are just small perturbations of the
coefficients of the power series in 5.1.11 on page 229.
The sage docstring for exponential_function_1 (which is ultimately
implemented in PARI) says:
REFERENCE: See page 262, Prop 5.6.12, of Cohen's book "A Course
in Computational Algebraic Number Theory".
where Cohen suggests using equation 5.1.11 from A&S for x small (he says
x <= 4) and the continued fraction expansion - equation 5.1.22 - for x
large.
On Thu, 2008-01-17 at 10:17 -0600, [EMAIL PROTECTED] wrote:
> The A&S handbook lists polynomial coefficients for approximation of E1,
> the exponential integral. Does anyone know how these coefficients were
> derived? Is it a chebyshev polynomial? I want to dynamically compute
> these coefficients to the required precision.
>
> Tim
>
> >
>
>
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