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1 13th April 01:10
vladimir bondarenko
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Posts: 1
Default An exact 1-D integration challenge - 19 - we mean, a challenge for Maple...


Hello the symbolic computation ladies and gentlemen ,

Is there a person who can show how to calculate using a set of
Maple operations the exact value of the following integral

int(hypergeom([-1/2, 1/4],[1/2],z/2)/(z-z^2)^(1/4), z= 0..1);

?

(I'd propose you don't waste much time with identify() here


Best wishes,

Vladimir Bondarenko

VM and GEMM architect
Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester, LLC
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2 13th April 01:10
c w
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Posts: 1
Default An exact 1-D integration challenge - 19 - we mean, a challenge forMaple...


Is it :
2*GAMMA(3/4)^2/Pi^(1/2)*hypergeom([3/4, 1/4, -1/2],[3/2, 1/2],1/2); ?
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3 13th April 01:37
vladimir bondarenko
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Posts: 1
Default An exact 1-D integration challenge - 19 - we mean, a challenge for Maple...


C W <sylvest...@ns.sympatico.ca>
writes on Thu, Mar 30 2006 4:56 am

CW> Is it :
CW> 2*GAMMA(3/4)^2/Pi^(1/2)*hypergeom([3/4, 1/4, -1/2],
CW> [3/2, 1/2],1/2);


Gee!


evalf(2*GAMMA(3/4)^2/Pi^(1/2)*hypergeom([3/4, 1/4, -1/2], [3/2,
1/2],1/2), 60);

evalf(-1/8*(3*ln(2)-2^(1/2)*(4-2*2^(1/2))^(1/2)+4*(4-2*2^(1/2)
)^(1/2)+2^(1/2)*(4+2*2^(1/2))^(1/2)+4*(4+2*2^(1/2))^(1/2)-2*ln
(2+(4-2*2^(1/2))^(1/2))-2*ln(2+(4+2*2^(1/2))^(1/2))-4*2^(1/4)*
(2^(1/2)+1)^(1/2)-8*2^(3/4)*(2^(1/2)+1)^(1/2)+4*ln(2^(1/4)+(2^
(1/2)+1)^(1/2)))*2^(1/2)*GAMMA(3/4)^2/Pi^(1/2), 60);


evalf(Int(hypergeom([-1/2, 1/4], [1/2], z/2)/(z-z^2)^(1/4), z=
0..1), 60);

1.578967212143193551704970999792714214037750532724 17210529762

1.578967212143193551704970999792714214037750532724 17210529761

1.578967212143193551704970999792714214037750532724 17210529762


It would be great if you think you could tell us the train of
your thoughts...

;-)
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