Re: Logrithmic Integral, Pi(x)

["cino hilliard" <hillcino368@hotmail.com>]

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

> From: "cino hilliard" <hillcino368@hotmail.com>
> To: pari-users@list.cr.yp.to
> 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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