cino hilliard on Tue, 27 Jan 2004 19:38:55 +0100

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Re: Logrithmic Integral, Pi(x)

"Behavior is not for the pursuit of survival but because of it."

From: "cino hilliard" <>
Subject: Re: Logrithmic Integral, Pi(x)
Date: Sun, 11 Jan 2004 22:39:06 +0000

GP/PARI CALCULATOR Version 2.2.7 (development CHANGES-1.844)
      i686 running cygwin (ix86 kernel) 32-bit version
     compiled: Oct 28 2003, gcc-3.3.1 (cygming special)
      (readline v4.3 enabled, extended help available)

Hi Karim,
Recently I had a need for the Logarithmic Integral. I could not find it in Pari. Here is my rendition. I am assuming Euler() is similar to the Euler2() below which has the zeta function. It seems to be working ok at least compared to Maple. Can you implement an Li, Ei function?

The Li function can be obtained from Pari with Li(x) = -einti(log(1/x))

einti(x) is the same as maple Ei(1,x)
But I cannot duplicate maple Ei(x)
Pi(10^22) = 783964159847056303858
19:10) gp > Li(4*10^22) - 783964159847056303858
%33 = 5101648384.715526417
%32 = 783964159852157952242.7155264
19:10) gp > Li(4*10^22) - 783964159847056303858
%33 = 5101648384.715526417

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