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 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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