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Science Forum Index » Math - Symbolic Forum » Solving Integrals with the Quantum Computer Algebra...
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| Vladimir Bondarenko... |
 Posted: Mon May 05, 2008 7:36 pm |
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http://www.planetquantum.com/News/080501.htm
Since our successful publication of 100,000+ hypergeometric
formulas, we have tasked ourselves with the new challenging
goal of online publication of 100,000+ integrals at the same
difficulty level as integrals which can be found in famous
integral tables such as Gradshteyn, I. S. and Ryzhik, I. M.
and Prudnikov, A. P., Brychkov, Yu. A., Marichev, O. I. |
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| galathaea... |
| Posted: Mon May 05, 2008 8:24 pm |
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On May 5, 10:36 pm, Vladimir Bondarenko <v... at (no spam) cybertester.com> wrote:
Quote: http://www.planetquantum.com/News/080501.htm
Since our successful publication of 100,000+ hypergeometric
formulas, we have tasked ourselves with the new challenging
goal of online publication of 100,000+ integrals at the same
difficulty level as integrals which can be found in famous
integral tables such as Gradshteyn, I. S. and Ryzhik, I. M.
and Prudnikov, A. P., Brychkov, Yu. A., Marichev, O. I.
it is cool how they ordered their hypergeometric list
http://www.planetquantum.com/HyperF/FTable1F2NZ7/Page1.htm
the ability to see the fractions like that
and why the rational points are so "integrable"
(in one abuse of the term)
is important to the whole hypergeometric endeavor
using tables like theirs
larger scale patterns become easier to see
for instance
one might notice that formulae for
H (A, B; x)
p q
appear to relate to formulae for
H ( (X) (A+i)/n, (X) (B+j)/n; x^n * n^s)
np nq
in that many of the arguments and coefficients are the same
but the functions slightly different
one might realise that this is related to the fact that
|m
| H
|n p q
is a np_H_nq with these fractional parameters
and can be expressed as a sum at the cyclotomic multiples of x
in the standard simpson multisection form
tools like this quantum CAS
(windows only and pretty crappy looking if you ask me)
are opening up the ability to map large scale structures
mapping hypergeometrics has been slow but very fruitful
there is a lot of structure there
using multisection and contiguous relations on one of these CAS
and we suddenly can walk over the many rational places of H
and the integer symmetries fold into the rationals
a basis has been given
and the 1_H_1 - 2_H_2 similarities
can be seen as just an instance of a much more general symmetry
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galathaea: prankster, fablist, magician, liar |
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