I made a few modifications so it now works everywhere but (0,1) On Jun 11, 1:45 pm, "William Stein" <[EMAIL PROTECTED]> wrote: > 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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