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From: Vladimir Bondarenko on 2 Aug 2010 06:23
Hello,

Mathematica:

I - I Sqrt[2 Pi] EllipticE[2]/Gamma[3/4]^2

Maple:

I-I*sqrt(2*Pi)*EllipticE(sqrt(2))/GAMMA(3/4)^2

Can you "elementarize" this ?

Cheers,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

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

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"...... the challenges imply that a solution is built within the
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From: Vladimir Bondarenko on 3 Aug 2010 21:10
On Aug 2, 2:34 pm, Axel Vogt <&nore...(a)axelvogt.de> wrote:
> Vladimir Bondarenko wrote:
> > Hello,
>
> > Mathematica:
>
> > I - I Sqrt[2 Pi] EllipticE[2]/Gamma[3/4]^2
>
> > Maple:
>
> > I-I*sqrt(2*Pi)*EllipticE(sqrt(2))/GAMMA(3/4)^2
>
> > Can you "elementarize" this ?
>
> Numerics suggest it equals 1, thus one wants to show:
>
> sqrt(2*Pi)*EllipticE(sqrt(2))= (1+I)*GAMMA(3/4)^2.
>
> Writing EllipticE as integral shows, that one has the
> following identity:   sqrt(2)* EllipticE(sqrt(2)) =
> '(1+I)*(2*EllipticE(1/sqrt(2))-EllipticK(1/sqrt(2)))'
>
> Or otherwise said: the following should hold true
>
> (2*EllipticE(1/sqrt(2))-EllipticK(1/sqrt(2))) =
>     GAMMA(3/4)^2/sqrt(Pi);
>
> Converting to hypergeometrics and simplifying does it:
>
>    convert(%, hypergeom);
>    simplify(%);
>    is(%);
>
>                      true
>
> PS: it does not make *any* sense to post such to the
> numerical or Matlab group, as you want _non-numerical_
> answers.

"PS: it does not make *any* sense to post such to the
numerical or Matlab group, as you want _non-numerical_
answers."

Yes, the symbolic ones.

We own a MATLAB 7 copy from the MathWorks, there is
a symbolic toolboox in MATLAB. Now it is presented
by MuPAD 4.

Also, we discovered that there are readers in
sci.math.num-analysis who by some reasons are
interested in symbolic answers...

:)
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