On Wed, Jun 11, 2008 at 8:07 AM, M. Yurko <[EMAIL PROTECTED]> wrote:
>
> O.K. I defined li(x) as follows:
>
> def li(z): #def log integral for real and complex variables
> if z in RR and z >= 2: #check if real number greater than 2
> return Li(z) +
> 1.045163780117492784844588889194613136522615578151 #adjust for offset
> in SAGE def
> elif z == 1:
> return -infinity
> else: #mode for complex and below 2 from incomplete gamma
> z = CDF(z)
> return -gamma_inc(0,-log(z)) + (log(log(z))-log(1/log(z)))/2-
> log(-log(z))
>
> The first part uses SAGE's built in Li(x) but adjusts for the offset.
> The second part should be self explanatory. The third part uses a
> formula involving the incomplete gamma function which I found on the
> Wolfram Functions website. On testing different values with an
> external calculator, the third statement appears to only be valid for
> negative reals and complex numbers. This leaves the interval [0,2)
> undefined. Please note that I have no background in complex analysis
> and that my above statements about domain are only based upon
> experimentation.
>
> --
I've made a trac ticket for this:
http://trac.sagemath.org/sage_trac/ticket/3401
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