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Vladimir Bondarenko
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 Posted: Mon Jul 21, 2008 6:56 am Post subject: An exact simplification challenge - 66 (MeijerG) |
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Hello,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
?
Best wishes,
Vladimir Bondarenko
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
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"We must understand that technologies
like these are the way of the future."
------------------------------------------------------ |
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Mate
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| Posted: Mon Jul 21, 2008 6:10 pm Post subject: Re: An exact simplification challenge - 66 (MeijerG) |
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On Jul 21, 9:56 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]Hello,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
[/quote]
You can try also:
MeijerG([[], []],[[89/55, 78/55, 67/55, 56/55, 9/11], []],10/7)
MeijerG([[], []],[[113/60, 101/60, 89/60, 77/60, 13/12], []],1/2)
MeijerG([[], []],[[93/85, 76/85, 59/85, 42/85, 5/17], []],2)
MeijerG([[], []],[[73/60, 61/60, 49/60, 37/60, 5/12], []],4)
MeijerG([[], []],[[53/60, 41/60, 29/60, 17/60, 1/12], []],9/14)
MeijerG([[], []],[[5/3, 22/15, 19/15, 16/15, 13/15], []],17/9)
MeijerG([[], []],[[138/85, 121/85, 104/85, 87/85, 14/17], []],4/3)
MeijerG([[], []],[[93/85, 76/85, 59/85, 42/85, 5/17], []],2)
MeijerG([[], []],[[37/15, 34/15, 31/15, 28/15, 5/3], []],1/4)
MeijerG([[], []],[[71/45, 62/45, 53/45, 44/45, 7/9], []],1/9)
MeijerG([[], []],[[88/85, 71/85, 54/85, 37/85, 4/17], []],9/5)
MeijerG([[], []],[[29/5, 28/5, 27/5, 26/5, 5], []],13/2)
MeijerG([[], []],[[24/5, 23/5, 22/5, 21/5, 4], []],5)
MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],1/6)
MeijerG([[], []],[[111/20, 107/20, 103/20, 99/20, 19/4], []],1/2)
MeijerG([[], []],[[104/55, 93/55, 82/55, 71/55, 12/11], []],7/17)
MeijerG([[], []],[[73/35, 66/35, 59/35, 52/35, 9/7], []],10/9)
MeijerG([[], []],[[166/95, 147/95, 128/95, 109/95, 18/19], []],6)
MeijerG([[], []],[[78/35, 71/35, 64/35, 57/35, 10/7], []],1/2)
MeijerG([[], []],[[72/65, 59/65, 46/65, 33/65, 4/13], []],13/5)
MeijerG([[], []],[[1, 4/5, 3/5, 2/5, 1/5], []],3/7)
MeijerG([[], []],[[67/40, 59/40, 51/40, 43/40, 7/8], []],3/8)
MeijerG([[], []],[[116/45, 107/45, 98/45, 89/45, 16/9], []],9/14)
MeijerG([[], []],[[82/15, 79/15, 76/15, 73/15, 14/3], []],17/15)
MeijerG([[], []],[[136/95, 117/95, 98/95, 79/95, 12/19], []],3/8)
MeijerG([[], []],[[88/85, 71/85, 54/85, 37/85, 4/17], []],17/6)
MeijerG([[], []],[[41/20, 37/20, 33/20, 29/20, 5/4], []],17/4)
MeijerG([[], []],[[22/15, 19/15, 16/15, 13/15, 2/3], []],8/7)
MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],10)
MeijerG([[], []],[[137/65, 124/65, 111/65, 98/65, 17/13], []],9/5)
MeijerG([[], []],[[141/70, 127/70, 113/70, 99/70, 17/14], []],4/5)
MeijerG([[], []],[[11/5, 2, 9/5, 8/5, 7/5], []],19/3)
MeijerG([[], []],[[9/5, 8/5, 7/5, 6/5, 1], []],20/9)
MeijerG([[], []],[[31/20, 27/20, 23/20, 19/20, 3/4], []],1/6)
MeijerG([[], []],[[54/5, 53/5, 52/5, 51/5, 10], []],14/3)
MeijerG([[], []],[[17/15, 14/15, 11/15, 8/15, 1/3], []],4)
MeijerG([[], []],[[13/5, 12/5, 11/5, 2, 9/5], []],1/3)
MeijerG([[], []],[[73/35, 66/35, 59/35, 52/35, 9/7], []],13/2)
MeijerG([[], []],[[17/15, 14/15, 11/15, 8/15, 1/3], []],1/2)
MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],2/3) |
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Vladimir Bondarenko
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| Posted: Mon Jul 21, 2008 6:50 pm Post subject: Re: An exact simplification challenge - 66 (MeijerG) |
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On Jul 21, 11:10 am, Mate <mmat...@personal.ro> wrote:
[quote]On Jul 21, 9:56 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
Hello,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
You can try also:
MeijerG([[], []],[[89/55, 78/55, 67/55, 56/55, 9/11], []],10/7)
MeijerG([[], []],[[113/60, 101/60, 89/60, 77/60, 13/12], []],1/2)
MeijerG([[], []],[[93/85, 76/85, 59/85, 42/85, 5/17], []],2)
MeijerG([[], []],[[73/60, 61/60, 49/60, 37/60, 5/12], []],4)
MeijerG([[], []],[[53/60, 41/60, 29/60, 17/60, 1/12], []],9/14)
MeijerG([[], []],[[5/3, 22/15, 19/15, 16/15, 13/15], []],17/9)
MeijerG([[], []],[[138/85, 121/85, 104/85, 87/85, 14/17], []],4/3)
MeijerG([[], []],[[93/85, 76/85, 59/85, 42/85, 5/17], []],2)
MeijerG([[], []],[[37/15, 34/15, 31/15, 28/15, 5/3], []],1/4)
MeijerG([[], []],[[71/45, 62/45, 53/45, 44/45, 7/9], []],1/9)
MeijerG([[], []],[[88/85, 71/85, 54/85, 37/85, 4/17], []],9/5)
MeijerG([[], []],[[29/5, 28/5, 27/5, 26/5, 5], []],13/2)
MeijerG([[], []],[[24/5, 23/5, 22/5, 21/5, 4], []],5)
MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],1/6)
MeijerG([[], []],[[111/20, 107/20, 103/20, 99/20, 19/4], []],1/2)
MeijerG([[], []],[[104/55, 93/55, 82/55, 71/55, 12/11], []],7/17)
MeijerG([[], []],[[73/35, 66/35, 59/35, 52/35, 9/7], []],10/9)
MeijerG([[], []],[[166/95, 147/95, 128/95, 109/95, 18/19], []],6)
MeijerG([[], []],[[78/35, 71/35, 64/35, 57/35, 10/7], []],1/2)
MeijerG([[], []],[[72/65, 59/65, 46/65, 33/65, 4/13], []],13/5)
MeijerG([[], []],[[1, 4/5, 3/5, 2/5, 1/5], []],3/7)
MeijerG([[], []],[[67/40, 59/40, 51/40, 43/40, 7/8], []],3/8)
MeijerG([[], []],[[116/45, 107/45, 98/45, 89/45, 16/9], []],9/14)
MeijerG([[], []],[[82/15, 79/15, 76/15, 73/15, 14/3], []],17/15)
MeijerG([[], []],[[136/95, 117/95, 98/95, 79/95, 12/19], []],3/8)
MeijerG([[], []],[[88/85, 71/85, 54/85, 37/85, 4/17], []],17/6)
MeijerG([[], []],[[41/20, 37/20, 33/20, 29/20, 5/4], []],17/4)
MeijerG([[], []],[[22/15, 19/15, 16/15, 13/15, 2/3], []],8/7)
MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],10)
MeijerG([[], []],[[137/65, 124/65, 111/65, 98/65, 17/13], []],9/5)
MeijerG([[], []],[[141/70, 127/70, 113/70, 99/70, 17/14], []],4/5)
MeijerG([[], []],[[11/5, 2, 9/5, 8/5, 7/5], []],19/3)
MeijerG([[], []],[[9/5, 8/5, 7/5, 6/5, 1], []],20/9)
MeijerG([[], []],[[31/20, 27/20, 23/20, 19/20, 3/4], []],1/6)
MeijerG([[], []],[[54/5, 53/5, 52/5, 51/5, 10], []],14/3)
MeijerG([[], []],[[17/15, 14/15, 11/15, 8/15, 1/3], []],4)
MeijerG([[], []],[[13/5, 12/5, 11/5, 2, 9/5], []],1/3)
MeijerG([[], []],[[73/35, 66/35, 59/35, 52/35, 9/7], []],13/2)
MeijerG([[], []],[[17/15, 14/15, 11/15, 8/15, 1/3], []],1/2)
MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],2/3)
[/quote]
I feel sorry that you seem do not feel the difference.
These you quote are not a challenge for Mathematica.
It cracks them via FunctionExpand.
But Mathematica 6.0.3 cannot simplify the Cyber Tester>s one,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
Now you can? |
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Axel Vogt
Guest
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| Posted: Tue Jul 22, 2008 1:38 am Post subject: Re: An exact simplification challenge - 66 (MeijerG) |
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Vladimir Bondarenko wrote:
[quote]On Jul 21, 11:10 am, Mate <mmat...@personal.ro> wrote:
On Jul 21, 9:56 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
Hello,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
You can try also:
.... (various omitted)
....
But Mathematica 6.0.3 cannot simplify the Cyber Tester>s one,
[/quote]
The (formal) problem is the argument x=1 as in most of the tasks.
Maple is far from good on MeijerG ... Instead of jumping into the
work (say: reading Adamchik, Marichev or the definitions and then
fighting with Mellin transforms) one can try to convert to sums
or hypergeometrics (finally approaching x=1).
For the last way one get ~ 2F1 + 3F2, where both terms diverge in
x=1 (but probably may cancel to a finite value).
For that my 'suggestion' would be to use Euler>s integral & write
3F2 as Int(2F1) and for the 1st 2F1 to try a 'shifting' trick (as
it may be found in Lebedev 9.1.7) to reach the assumptions for
that integral representation. But I am too lame for that ... |
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Vladimir Bondarenko
Guest
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| Posted: Tue Jul 22, 2008 2:08 am Post subject: Re: An exact simplification challenge - 66 (MeijerG) |
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On Jul 21, 11:50 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]On Jul 21, 11:10 am, Mate <mmat...@personal.ro> wrote:
On Jul 21, 9:56 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
Hello,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
You can try also:
MeijerG([[], []],[[89/55, 78/55, 67/55, 56/55, 9/11], []],10/7)
[/quote]
[skipped]
[quote]MeijerG([[], []],[[23/10, 21/10, 19/10, 17/10, 3/2], []],2/3)
I feel sorry that you seem do not feel the difference.
These you quote are not a challenge for Mathematica.
It cracks them via FunctionExpand.
But Mathematica 6.0.3 cannot simplify the Cyber Tester>s one,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
Now you can?
[/quote]
By "challenge" (for CASs, as usually in our list of
challenges) I mean that
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
can be expressed in terms of elementary functions but the
modern CASs fail to accomplish this feat directly. :-(
Can we the human beings? ;) |
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Vladimir Bondarenko
Guest
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| Posted: Thu Jul 24, 2008 3:24 am Post subject: Re: An exact simplification challenge - 66 (MeijerG) |
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On Jul 20, 11:56 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]Hello,
MeijerG[{{-1, 0, 1/2}, {}}, {{-1/4, 0}, {-3/4}}, 1]
?
Best wishes,
Vladimir Bondarenko
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
------------------------------------------------------
"We must understand that technologies
like these are the way of the future."
------------------------------------------------------
[/quote]
Sqrt[Pi]/2 (4.....
:) |
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