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From: Vladimir Bondarenko on 11 Jul 2010 00:00
Hello,

Overnight, I had been tortured by a nightmare. I dreamed
that I was trying to simplify the following, in vain!..

-8+2/3*Pi^2-6*ln(2)^2+8*ln(2)+8*2^(1/2)+4*ln(-1+2^(1/2))-
4*ln(1+2^(1/2))+4*2^(1/2)*ln(5-2*6^(1/2))*ln(2)-4/3*2^(1/
2)*Pi^2+6*ln(1+2^(1/2))*ln(2)-2^(1/2)*ln(-2+6^(1/2))^2+2^
(1/2)*ln(2+6^(1/2))^2-2*I*2^(1/2)*Pi*ln(-2+6^(1/2))-4*2^(
1/2)*ln(2+6^(1/2))*ln(2)-2*I*ln(1+2^(1/2))*Pi+2*I*Pi*ln(2
)+8*hypergeom([-1/2,-1/2,-1/2],[1/2,1/2],-2)-4*polylog(2,
1/2+1/2*2^(1/2))-4*2^(1/2)*ln(5-2*6^(1/2))-2*I*Pi*2^(1/2)
*ln(2)+4*2^(1/2)*polylog(2,1/2+1/4*2^(1/2)*3^(1/2))+2*ln(
1-2^(1/2))*ln(2)-2*ln(1-2^(1/2))*ln(1+2^(1/2))+8*2^(1/2)*
ln(2)^2-4*2^(1/2)*ln(2-6^(1/2))*ln(2)+2*2^(1/2)*ln(2-6^(1
/2))*ln(2+6^(1/2))-hypergeom([1/2,1,1,1],[2,2,2],-1)

But in the end, Pythagoras came to me and said something,
and I breathed a sigh of relief.

Can you restore Mr. Py's processing?

Cheers,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

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"We must understand that technologies
like these are the way of the future."

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http://groups.google.com/group/sci.math/msg/9f429c3ea5649df5

"...... the challenges imply that a solution is built within the
framework of the existent CAS functions & built-in definitions."

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From: clicliclic on 12 Jul 2010 10:04

Vladimir Bondarenko schrieb:
>
>
> Overnight, I had been tortured by a nightmare. I dreamed
> that I was trying to simplify the following, in vain!..
>
> -8+2/3*Pi^2-6*ln(2)^2+8*ln(2)+8*2^(1/2)+4*ln(-1+2^(1/2))-
> 4*ln(1+2^(1/2))+4*2^(1/2)*ln(5-2*6^(1/2))*ln(2)-4/3*2^(1/
> 2)*Pi^2+6*ln(1+2^(1/2))*ln(2)-2^(1/2)*ln(-2+6^(1/2))^2+2^
> (1/2)*ln(2+6^(1/2))^2-2*I*2^(1/2)*Pi*ln(-2+6^(1/2))-4*2^(
> 1/2)*ln(2+6^(1/2))*ln(2)-2*I*ln(1+2^(1/2))*Pi+2*I*Pi*ln(2
> )+8*hypergeom([-1/2,-1/2,-1/2],[1/2,1/2],-2)-4*polylog(2,
> 1/2+1/2*2^(1/2))-4*2^(1/2)*ln(5-2*6^(1/2))-2*I*Pi*2^(1/2)
> *ln(2)+4*2^(1/2)*polylog(2,1/2+1/4*2^(1/2)*3^(1/2))+2*ln(
> 1-2^(1/2))*ln(2)-2*ln(1-2^(1/2))*ln(1+2^(1/2))+8*2^(1/2)*
> ln(2)^2-4*2^(1/2)*ln(2-6^(1/2))*ln(2)+2*2^(1/2)*ln(2-6^(1
> /2))*ln(2+6^(1/2))-hypergeom([1/2,1,1,1],[2,2,2],-1)
>
> But in the end, Pythagoras came to me and said something,
> and I breathed a sigh of relief.
>
> Can you restore Mr. Py's processing?
>

Vladimir is getting impatient and WRI's Oleksandr seems to be on
holyday. Fortunately, I had a dream last night, and in the dream I could
play with Derive 13. I typed in

FPQ([-1/2,-1/2,-1/2],[1/2,1/2],-2)

and it responded with

SQRT(2)*DILOG(SQRT(3)+SQRT(2)+1)-SQRT(2)*DILOG(SQRT(3)+SQRT(2))+~
SQRT(2)*LN(SQRT(3)+SQRT(2))*LN(SQRT(3)+SQRT(2)+1)-SQRT(2)*LN(SQR~
T(3)+SQRT(2))^2/2-SQRT(2)*LN(SQRT(3)+SQRT(2))+SQRT(2)*pi^2/12+SQ~
RT(3)

which approximates to

1.957255245

and I typed in

FPQ([1/2,1,1,1],[2,2,2],-1)

and it responded with

4*DILOG(SQRT(2)/2+1/2)-8*LN(SQRT(2)/2+1/2)-4*LN(2)*LN(SQRT(2)-1)~
-2*LN(SQRT(2)-1)^2-2*LN(2)^2+8*SQRT(2)-8

which approximates to

0.947963376

I dawned upon me that this version of Derive was still using DILOG()
with the old-fashioned definition DILOG(z) = POLYLOG(2,1-z). About this
fact I became so agitated that I woke and realized I had been dreaming.
But I was able to reproduce the results although I could no longer
access Derive 13.

Martin.

PS: I have removed sci.math.num-analysis and comp.soft-sys.matlab
because aioe.org allows no more than three groups.
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