clicliclic@[EMAIL PROTECTED]
wrote:
> Vladimir Bondarenko schrieb:
> >
> > Hello CAS Fan the Earthling,
> >
> > [...] is there an Audacious Warrior the Simplifier to come up with
> > a sequence of CAS commands to "elementarize" this
> >
> > LerchPhi(1/9, 2, 1/2) - 3*dilog(3/4)
> >
>
> Derive 8.07
Fascinating! Where can I get a copy of Derive 8.07 ?
David
> handles this automatically in a fraction of a second as follows:
>
> LERCH_PHI(1/9,2,1/2)-3*DILOG(3/4)
>
> " -> "
>
> 2*(LERCH_PHI(1/3,2,1)+LERCH_PHI(-1/3,2,1))-3*DILOG(3/4)
>
> " -> "
>
> 2*(DILOG(2/3)/(1/3)+DILOG(4/3)/(-1/3))-3*DILOG(3/4)
>
> " -> "
>
> 2*(3*(-DILOG(3/2)-LN(2/3)^2/2)-3*DILOG(4/3))-3*DILOG(3/4)
>
> " -> "
>
> -6*DILOG(4/3)-6*DILOG(3/2)-3*LN(3)^2+6*LN(2)*LN(3)-3*LN(2)^2-3*(-
> DILOG(4/3)-L~
> N(3/4)^2/2)
>
> " -> "
>
> -6*DILOG(4/3)-6*DILOG(3/2)-3*LN(3)^2+6*LN(2)*LN(3)-3*LN(2)^2-3*(-
> DILOG(4/3)-(~
> LN(3)-2*LN(2))^2/2)
>
> -3*DILOG(4/3)-6*DILOG(3/2)-3*LN(3)^2/2+3*LN(2)^2
>
> Numerically, this approximates to 3.248520221. There are obvious
> problems with the rule strings here. Also note that Derive assumes
> dilog(z) = Li_2(1-z); cf. Wikipedia at <http://en.wikipedia.org/wiki/
> Polylogarithm>.
>
> Martin.
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