Telescoping in the context of symbolic summation in Maple

Абрамов, С. А.; Carette, Jacques; Geddes, K. O.; Le, H. Q.

doi:10.1016/j.jsc.2003.08.010

Cited by 15 publications

(19 citation statements)

References 18 publications

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“…Staying below the above hyperbola, we have obtained, at q = 11 and µ = 9 which requires 185 terms in the series, two linearly independent differential equations that satisfy the remaining 30 terms of the series. The combination of these two differential equations gives (24) which has been checked to be of minimal order. Note the fact that besides the Fuchsian differential equation of minimal order with an apparent polynomial, there are other differential equations of higher order that require less terms in the series to be identified.…”

Section: Series Generationmentioning

confidence: 99%

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Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties

Zenine¹,

Boukraa²,

Hassani³

et al. 2005

J. Phys. A: Math. Gen.

184

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We give the Fuchsian linear differential equation satisfied by χ (4) , the "four-particle" contribution to the susceptibility of the isotropic square lattice Ising model. This Fuchsian differential equation is deduced from a series expansion method introduced in two previous papers and is applied with some symmetries and tricks specific to χ (4) . The corresponding order ten linear differential operator exhibits a large set of factorization properties. Among these factorizations one is highly remarkable: it corresponds to the fact that the two-particle contribution χ (2) is actually a solution of this order ten linear differential operator. This result, together with a similar one for the order seven differential operator corresponding to the three-particle contribution, χ (3) , leads us to a conjecture on the structure of all the n-particle contributions χ (n) .

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Section: Series Generationmentioning

confidence: 99%

“…With these five solutions corresponding to three differential operators of order one, and one differential operator of order two, it is easy to construct 24 factorizations of L 10 , the differential operator corresponding to the Fuchsian differential equation (24), which can be written ¶ as :…”

Section: Properties Of the Fuchsian Differential Equation (24)mentioning

confidence: 99%

Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties

Zenine¹,

Boukraa²,

Hassani³

et al. 2005

J. Phys. A: Math. Gen.

184

View full text Add to dashboard Cite

show abstract

“…This is why, for instance, computer algebra implementations of algorithms for hypergeometric summation [16,15,1] enjoy a large and still increasing community of users with a broad variety of different backgrounds. Even more so than in the ordinary case, computations in q-calculus tend to involve large expressions that can be tackled by computer algebra much faster and much more reliably than by hand.…”

Section: Introductionmentioning

confidence: 99%

A Mathematica package for q-holonomic sequences and power series

Kauers

Koutschan

2009

Ramanujan J

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Abstract. We describe a Mathematica package for dealing with q-holonomic sequences and power series. The package is intended as a q-analogue of the Maple package gfun and the Mathematica package GeneratingFunctions. It provides commands for addition, multiplication, and substitution of these objects, for converting between various representations (q-differential equations, q-recurrence equations, q-shift equations), for computing sequence terms and power series coefficients, and for guessing recurrence equations given initial terms of a sequence.

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“…This general summation strategy is explained in detail for hypergeometric summation in [19]. Implementations of these algorithms are available since long [18,1]. The same technique is applicable for more general expressions.…”

Section: Pldes and Summationmentioning

confidence: 99%

Application of unspecified sequences in symbolic summation

Kauers

Schneider

2006

Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation

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We consider symbolic sums which contain subexpressions representing unspecified sequences. Existing symbolic summation technology is extended to sums of this kind. We show how this can be applied in the systematic search for general summation identities. Both, results about the non-existence of identities of a certain form, and examples of general families of identities which we have discovered automatically are included in the paper.

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Telescoping in the context of symbolic summation in Maple

Cited by 15 publications

References 18 publications

Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties

Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties

A Mathematica package for q-holonomic sequences and power series

Application of unspecified sequences in symbolic summation

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About

Telescoping in the context of symbolic summation in Maple

Cited by 15 publications

References 18 publications

Ising model susceptibility: the Fuchsian differential equation for χ(4)and its factorization properties

Ising model susceptibility: the Fuchsian differential equation for χ(4)and its factorization properties

A Mathematica package for q-holonomic sequences and power series

Application of unspecified sequences in symbolic summation

Contact Info

Product

Resources

About

Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties

Ising model susceptibility: the Fuchsian differential equation for χ⁽⁴⁾and its factorization properties