Search Results - "Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)"

On the Existence of Telescopers for P-Recursive Sequences: On the existence of telescopers for P-recursive sequences

Authors: Lixin Du

Source: Journal of Symbolic Computation. 130:102423

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, integral bases, Generalized hypergeometric series, \({}_pF_q\), Abramov-Petkovšek reduction, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, 68W30, 12H10, 33F10, 39A06, 68W40, symbolic summation

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Access URL: http://arxiv.org/abs/2311.06065
https://zbmath.org/8019241
https://doi.org/10.1016/j.jsc.2025.102423

On linearization coefficients of Jacobi polynomials

Authors: Hamza Chaggara Wolfram Koepf

Source: Applied Mathematics Letters. 23:609-614

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Linearization coefficients, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Jacobi polynomials, Reduction formulae, 0101 mathematics, reduction formulae, 01 natural sciences, linearization coefficients

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Access URL: http://www.mathematik.uni-kassel.de/~koepf/Publikationen/ChaggaraKoepf2010.pdf
https://www.sciencedirect.com/science/article/pii/S0893965910000236
https://core.ac.uk/display/22585498
https://www.sciencedirect.com/science/article/abs/pii/S0893965910000236
https://dblp.uni-trier.de/db/journals/appml/appml23.html#ChaggaraK10

Elimination in Weyl Algebra and q-Identities: Elimination in Weyl algebra and \(q\)-identities

Authors: Tianming Wang Yujuan Huang

Source: Journal of Systems Science and Complexity. 20:601-609

Subject Terms: Basic hypergeometric functions, Zeilberger algorithm, algorithmic proof of hypergeometric identities, \(q\)-calculus and related topics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2114020
https://link.springer.com/content/pdf/10.1007/s11424-007-9058-6.pdf
https://link.springer.com/article/10.1007/s11424-007-9058-6
https://dblp.uni-trier.de/db/journals/jossac/jossac20.html#HuangW07

MOPS: Multivariate orthogonal polynomials (symbolically): MOPS: multivariate orthogonal polynomials (symbolically)

Authors: Ioana Dumitriu Gene Shuman Alan Edelman

Source: Journal of Symbolic Computation. 42:587-620

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computational Mathematics, Algebra and Number Theory, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), Numerical approximation and evaluation of special functions, 0101 mathematics, Symbolic computation and algebraic computation, 15A52, 46N99, 01 natural sciences, Mathematical Physics

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Access URL: http://arxiv.org/abs/math-ph/0409066
https://zbmath.org/5205232
https://doi.org/10.1016/j.jsc.2007.01.005

On the order of the recurrence produced by the method of creative telescoping

Authors: H. Q. Le Sergei A. Abramov

Source: Discrete Mathematics. 298:2-17

Subject Terms: Minimal telescoper, Hypergeometric term, Lower bound, Zeilberger's algorithm, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Discrete Mathematics and Combinatorics, Additive decomposition, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Theoretical Computer Science

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Access URL: https://zbmath.org/2207447
https://doi.org/10.1016/j.disc.2004.05.018
https://www.sciencedirect.com/science/article/pii/S0012365X0500230X#!
https://dblp.uni-trier.de/db/journals/dm/dm298.html#AbramovL05
http://www.cecm.sfu.ca/CAG/papers/haledisc.pdf
https://core.ac.uk/display/82811990
https://www.sciencedirect.com/science/article/abs/pii/S0012365X0500230X
https://www.sciencedirect.com/science/article/pii/S0012365X0500230X

The q-Markov-WZ Method: The \(q\)-Markov-WZ method

Authors: Mohamud Mohammed

Source: Annals of Combinatorics. 9:205-221

Subject Terms: series convergence, Generalized hypergeometric series, \({}_pF_q\), Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), WZ theory, 0102 computer and information sciences, 0101 mathematics, Factorials, binomial coefficients, combinatorial functions, Software, source code, etc. for problems pertaining to special functions, 01 natural sciences, Combinatorial identities, bijective combinatorics

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Access URL: https://link.springer.com/article/10.1007/s00026-005-0252-8

Transformation on Infinite Double Series and Applications to Harmonic Number Identities: Transformation on infinite double series and applications to harmonic number identities

Authors: CHU, Wenchang DEDONNO L.

Source: Applicable Algebra in Engineering, Communication and Computing. 15:339-348

Subject Terms: Bernoulli Number, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Euler Number, 0102 computer and information sciences, Double Series Transformation, 0101 mathematics, Bernoulli and Euler numbers and polynomials, Catalan Constant, Binomial Coefficient Identity, Harmonic Number, 01 natural sciences, Combinatorial identities, bijective combinatorics

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Access URL: https://dblp.uni-trier.de/db/journals/aaecc/aaecc15.html#WenchangL05
https://link.springer.com/content/pdf/10.1007%2Fs00200-004-0165-5.pdf
https://link.springer.com/article/10.1007%2Fs00200-004-0165-5
https://hdl.handle.net/11587/103586

Expansion around half-integer values, binomial sums, and inverse binomial sums: Expansion around half-integer values, binomial sums, and inverse binomial sums.

Authors: Stefan Weinzierl

Source: Journal of Mathematical Physics. 45:2656-2673

Subject Terms: High Energy Physics - Theory, High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0103 physical sciences, FOS: Physical sciences, Numerical approximation and evaluation of special functions, Other Dirichlet series and zeta functions, 01 natural sciences

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Access URL: http://arxiv.org/pdf/hep-ph/0402131
http://arxiv.org/abs/hep-ph/0402131
https://ui.adsabs.harvard.edu/abs/2004JMP....45.2656W/abstract
https://core.ac.uk/display/25401096
https://aip.scitation.org/doi/full/10.1063/1.1758319
http://scitation.aip.org/content/aip/journal/jmp/45/7/10.1063/1.1758319
https://arxiv.org/abs/hep-ph/0402131
https://arxiv.org/pdf/hep-ph/0402131

k-free recurrences of double hypergeometric terms: \(k\)-free recurrences of double hypergeometric terms

Authors: Qing-Hu Hou

Source: Advances in Applied Mathematics. 32:468-484

Subject Terms: Holonomic function, hypergeometric term, k-free recurrence relation, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), holonomic function, Proper hypergeometric term, \(k\)-free recurrence relation, 0101 mathematics, Double hypergeometric term, 01 natural sciences

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Access URL: https://zbmath.org/2107249
https://doi.org/10.1016/s0196-8858(03)00056-3
https://www.sciencedirect.com/science/article/pii/S0196885803000563
https://doi.org/10.1016/S0196-8858(03)00056-3
https://www.sciencedirect.com/science/article/abs/pii/S0196885803000563
https://dblp.uni-trier.de/db/journals/aam/aam32.html#Hou04

COMPUTER PROOFS OF MATRIX PRODUCT IDENTITIES: Computer proofs of matrix product identities.

Authors: Peter J. Larcombe Burkhard Zimmermann Axel Riese

Source: Journal of Algebra and Its Applications. :105-109

Subject Terms: recurrence relations, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Matrix equations and identities, 0102 computer and information sciences, definite integration, computer proof, 0101 mathematics, Symbolic computation and algebraic computation, computer algebra, 01 natural sciences, indefinite rational matrix products

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Access URL: http://www.sfb013.uni-linz.ac.at/reports/2003/pdf-files/sfb03-11.pdf
https://www.worldscientific.com/doi/abs/10.1142/S0219498804000721

Liebe Opa Paul, ich bin auch ein experimental Scientist!: Liebe Opa Paul, ich bin auch ein experimental scientist!

Authors: Doron Zeilberger

Source: Advances in Applied Mathematics. 31:532-543

Subject Terms: Methodology of mathematics, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), History of linear algebra, 0102 computer and information sciences, 0101 mathematics, Symbolic computation and algebraic computation, General applied mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2012786
https://doi.org/10.1016/s0196-8858(03)00025-3
https://www.sciencedirect.com/science/article/abs/pii/S0196885803000253
https://www.sciencedirect.com/science/article/pii/S0196885803000253
https://dblp.uni-trier.de/db/journals/aam/aam31.html#Zeilberger03

Applications of Hermite transforms in computer algebra: Applications of Hermite transforms in computer algebra.

Authors: Helena Zakrajek

Source: Advances in Applied Mathematics. 31:301-320

Subject Terms: Hypergeometric polynomials, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Special integral transforms (Legendre, Hilbert, etc.), Rational functions, Linear differential equation, 0101 mathematics, 01 natural sciences, Hermite transform

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Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0196885803000137
https://dblp.uni-trier.de/db/journals/aam/aam31.html#Zakrajsek03
https://www.sciencedirect.com/science/article/pii/S0196885803000137#!

Computer proofs of a new family of harmonic number identities: Computer proofs of a new family of harmonic number identities.

Authors: Carsten Schneider Peter Paule

Source: Advances in Applied Mathematics. 31:359-378

Subject Terms: Binomial coefficients, factorials, \(q\)-identities, harmonic number, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), identities for binomial coefficients, 0102 computer and information sciences, 0101 mathematics, algorithms, 01 natural sciences, Number-theoretic algorithms, complexity

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Access URL: https://zbmath.org/2012777
https://doi.org/10.1016/s0196-8858(03)00016-2
https://www.risc.jku.at/publications/download/risc_200/HarmonicNumberIds.pdf
https://dblp.uni-trier.de/db/journals/aam/aam31.html#PauleS03
https://www.sciencedirect.com/science/article/pii/S0196885803000162
https://www.sciencedirect.com/science/article/abs/pii/S0196885803000162
http://www.risc.jku.at/publications/download/risc_200/HarmonicNumberIds.pdf
https://doi.org/10.1016/S0196-8858(03)00016-2

An improvement of the two-line algorithm for proving q-hypergeometric identities: An improvement of the two-line algorithm for proving \(q\)-hypergeometric identities.

Authors: Jie Li Bao-Yin Zhang

Source: Discrete Mathematics. 268:273-286

Subject Terms: Two-line algorithm, \(q\)-hypergeometric identities, Basic hypergeometric functions in one variable, \({}_r\phi_s\), two-line algorithm, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Sister Celine's technique, Discrete Mathematics and Combinatorics, sister Celine's technique, 0101 mathematics, q-Hypergeometric identities, 01 natural sciences, Combinatorial identities, bijective combinatorics, Theoretical Computer Science

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Access URL: https://zbmath.org/1956044
https://doi.org/10.1016/s0012-365x(02)00686-6
https://dblp.uni-trier.de/db/journals/dm/dm268.html#ZhangL03
https://www.sciencedirect.com/science/article/pii/S0012365X02006866
https://www.sciencedirect.com/science/article/abs/pii/S0012365X02006866
https://doi.org/10.1016/S0012-365X(02)00686-6

A combined symbolic and numerical algorithm for the computation of zeros of orthogonal polynomials and special functions

Authors: Javier Segura Amparo Gil

Source: Journal of Symbolic Computation. 35:465-485

Subject Terms: Orthogonal polynomials, Coulomb function, Fixed point iterations, Symbolic computation and algebraic computation, Maple algorithm, 01 natural sciences, Zeros, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Jacobi polynomial, Legendre polynomial, Special functions, three-term recurrence relation, Gegenbauer polynomial, Numerical approximation and evaluation of special functions, polynomial zeros, Bessel function, 0101 mathematics, orthogonal polynomials, numerical examples, Algebra and Number Theory, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Chebyshev polynomial, symbolic computation, special functions, Computational Mathematics, Computation of special functions and constants, construction of tables, fixed point iterations, Hermite polynomial, Numerical computation of solutions to single equations, conical functions, performance

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Access URL: https://zbmath.org/1968932
https://doi.org/10.1016/s0747-7171(03)00013-0
https://www.sciencedirect.com/science/article/abs/pii/S0747717103000130
https://www.sciencedirect.com/science/article/pii/S0747717103000130
https://dblp.uni-trier.de/db/journals/jsc/jsc35.html#GilS03

Computerized deconstruction: Computerized deconstruction.

Authors: Doron Zeilberger

Source: Advances in Applied Mathematics. 30:633-654

Subject Terms: Methodology of mathematics, Irrationality, linear independence over a field, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0102 computer and information sciences, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences

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Access URL: https://dl.acm.org/citation.cfm?id=782266.782269

When does Zeilberger's algorithm succeed?

Authors: Sergei A. Abramov

Source: Advances in Applied Mathematics. 30:424-441

Subject Terms: Zeilberger's algorithm, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/1981405
https://doi.org/10.1016/s0196-8858(02)00504-3
https://www.sciencedirect.com/science/article/pii/S0196885802005043
https://dblp.uni-trier.de/db/journals/aam/aam30.html#Abramov03
http://www.ccas.ru/sabramov/ps/Zsuccess.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0196885802005043

Computer Algebra and Computing Special Functions: Computer algebra and computing special functions

Authors: S. L. Skorokhodov

Source: Programming and Computer Software. 29:75-82

Subject Terms: symbolic transformations, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1023/A:1022944631820
https://dblp.uni-trier.de/db/journals/pcs/pcs29.html#Skorokhodov03

computer algebra and computing special functions: Computer algebra and computing special functions

Authors: S. L. Skorokhodov

Source: Programming and Computer Software. 29(2):75-82

Subject Terms: symbolic transformations, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Symbolic computation and algebraic computation

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/A:1022944631820
https://dblp.uni-trier.de/db/journals/pcs/pcs29.html#Skorokhodov03

A new elementary algorithm for proving q-hypergeometric identities: A new elementary algorithm for proving \(q\)-hypergeometric identities

Authors: Bao-Yin Zhang

Source: Journal of Symbolic Computation. 35:293-303

Subject Terms: computer proofs, Computational Mathematics, \(q\)-hypergeometric identities, elimination, Algebra and Number Theory, Elimination, Computer proofs, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0101 mathematics, q-Hypergeometric identities, 01 natural sciences, Combinatorial identities, bijective combinatorics

File Description: application/xml

Access URL: https://zbmath.org/1965170
https://doi.org/10.1016/s0747-7171(02)00136-0
https://www.sciencedirect.com/science/article/pii/S0747717102001360
https://dialnet.unirioja.es/servlet/articulo?codigo=319972
https://www.sciencedirect.com/science/article/abs/pii/S0747717102001360
https://dblp.uni-trier.de/db/journals/jsc/jsc35.html#Zhang03