Výsledky vyhledávání - Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)

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

Autoři: Javier Segura Amparo Gil

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

An extension of Zeilberger's fast algorithm to general holonomic functions

Autoři: Chyzak, Frédéric

Přispěvatelé: Chyzak, Frédéric

Zdroj: Discrete Mathematics. 217:115-134

Témata: Holonomic functions, [INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC], Zeilberger's algorithm, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0102 computer and information sciences, Symbolic computation and algebraic computation, 01 natural sciences, ∂-finite functions, Theoretical Computer Science, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], $\partial$-finite functions, hypergeometric sequences, holonomic functions, Gosper's algorithm, D-finite functions, Discrete Mathematics and Combinatorics, \(\partial\)-finite functions, Symbolic integration, Symbolic summation, Abramov's algorithm, 0101 mathematics, symbolic summation, Combinatorial identities, bijective combinatorics, symbolic integration

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: https://zbmath.org/1453348
https://doi.org/10.1016/s0012-365x(99)00259-9
https://inria.hal.science/hal-01069235v1
https://www.sciencedirect.com/science/article/pii/S0012365X99002599
https://doi.org/10.1016/S0012-365X(99)00259-9
https://dblp.uni-trier.de/db/journals/dm/dm217.html#Chyzak00
https://hal.inria.fr/hal-01069235/document
https://hal.inria.fr/hal-01069235

On the q-Analogue of Zeilberger's Algorithm to Rational Functions: On the \(q\)-analogue of Zeilberger's algorithm to rational functions

Autoři: H. Q. Le

Zdroj: Programming and Computer Software. 27:35-42

Témata: Basic hypergeometric functions, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0102 computer and information sciences, \(q\)-analogue of Zeilberger's algorithm, 0101 mathematics, 01 natural sciences, Combinatorial identities, bijective combinatorics

Popis souboru: application/xml

Přístupová URL adresa: https://dblp.uni-trier.de/db/journals/pcs/pcs27.html#Le01
https://link.springer.com/article/10.1023%2FA%3A1007186703355

A criterion for the applicability of Zeilberger's algorithm to rational functions

Autoři: Sergei A. Abramov H. Q. Le

Zdroj: Discrete Mathematics. 259:1-17

Témata: Linear difference and q-difference operators, hypergeometric term, rational function, linear difference operator, Zeilberger's algorithm, terminating condition, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Rational function, Terminating condition, Decomposition of indefinite sum, 01 natural sciences, Theoretical Computer Science, Hypergeometric term, Classical hypergeometric functions, \({}_2F_1\), decomposition of indefinite sum, \(q\)-difference operator, Discrete Mathematics and Combinatorics, 0101 mathematics

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1882138
https://doi.org/10.1016/s0012-365x(02)00442-9
https://dblp.uni-trier.de/db/journals/dm/dm259.html#AbramovL02
https://doi.org/10.1016/S0012-365X(02)00442-9
https://www.sciencedirect.com/science/article/pii/S0012365X02004429
https://www.sciencedirect.com/science/article/abs/pii/S0012365X02004429

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

Autoři: S. L. Skorokhodov

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

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

Popis souboru: application/xml

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

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

Autoři: Lixin Du

Zdroj: Journal of Symbolic Computation. 130:102423

Témata: 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

Popis souboru: application/xml

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

Multibasic and Mixed Hypergeometric Gosper-Type Algorithms: Multibasic and mixed hypergeometric Gosper-type algorithms

Autoři: Marko Petkovšek Andrej Bauer

Zdroj: Journal of Symbolic Computation. 28:711-736

Témata: Computational Mathematics, polynomial solutions of recurrence equations, Algebra and Number Theory, Bibasic functions and multiple bases, Gosper algorithm, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, greatest factorial factorization, hypergeometric solutions of equations

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1440298
https://doi.org/10.1006/jsco.1999.0321

When does Zeilberger's algorithm succeed?

Autoři: Sergei A. Abramov

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

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

Popis souboru: application/xml

Přístupová URL adresa: 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

Identities of nonterminating series by Zeilberger's algorithm

Autoři: Koornwinder, T.H.

Zdroj: Journal of Computational and Applied Mathematics. 99:449-461

Témata: Zeilberger algorithm, Gosper algorithm, 01 natural sciences, Saalschütz' summation formula, 0103 physical sciences, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Nonterminating hypergeometric series, Analysis of algorithms, 0101 mathematics, computer algebra, Generalized hypergeometric series, \({}_pF_q\), 68Q40, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), asymptotic estimates, \({_3F_2}\) hypergeometric series, 33C20, Computational Mathematics, Zeiberger's algorithm, Mathematics - Classical Analysis and ODEs, Computer algebra, WZ method, non-terminating hypergeometric series, Asymptotics

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/math/9805010
https://dare.uva.nl/personal/pure/en/publications/identities-of-nonterminating-series-by-zeilbergers-algorithm(006164b9-86b7-4ac5-924b-d8041f074ec3).html
https://hdl.handle.net/11245/1.149708
https://doi.org/10.1016/S0377-0427(98)00176-9
http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Computational%20And%20Applied%20Mathematics/Vol99.Issue1-2.1998/2633.pdf
http://www.sciencedirect.com/science/article/pii/S0377042798001769
https://www.sciencedirect.com/science/article/pii/S0377042798001769
https://www.narcis.nl/publication/RecordID/oai%3Adare.uva.nl%3Apublications%2F006164b9-86b7-4ac5-924b-d8041f074ec3

Algorithms forq -Hypergeometric Summation in Computer Algebra: Algorithms for \(q\)-hypergeometric summation in computer algebra

Autoři: Harald Böing Wolfram Koepf

Zdroj: Journal of Symbolic Computation. 28:777-799

Témata: Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), \(q\)-hypergeometric series, Algebra and Number Theory, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), \(q\)-Askey-Wilson polynomials, \(q\)-series, Symbolic computation and algebraic computation, 01 natural sciences, hypergeometric solutions of linear recurrence, Computational Mathematics, Computation of special functions and constants, construction of tables, Basic hypergeometric functions in one variable, \({}_r\phi_s\), Maple, Gosper and Zeilberger algorithms, 0101 mathematics

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1423190
https://doi.org/10.1006/jsco.1998.0339
https://www.sciencedirect.com/science/article/pii/S074771719890339X
https://doi.org/10.1006/jsco.1998.0339
http://www.mathematik.uni-kassel.de/~koepf/BoeingKoepf.pdf
https://opus4.kobv.de/opus4-zib/files/345/SC-98-02.pdf
https://dblp.uni-trier.de/db/journals/jsc/jsc28.html#BoingK99
https://dialnet.unirioja.es/servlet/articulo?codigo=477297

SFA, a Package on Symmetric Functions Considered as Operators over the Ring of Polynomials for the Computer Algebra System Maple: SFA, a package on symmetric functions considered as operators over the ring of polynomials for the computer algebra system MAPLE

Autoři: Prosper, V Prosper, V.

Přispěvatelé: Prosper, V Prosper, V.

Zdroj: Journal of Symbolic Computation. 29:83-94

Témata: ring of polynomials, Algebra and Number Theory, Faber polynomials, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Lagrange inversion, Symbolic computation and algebraic computation, 01 natural sciences, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computational Mathematics, Computation of special functions and constants, construction of tables, Maple, SFA package, Packaged methods for numerical algorithms, symmetric functions, 0101 mathematics, computer algebra

Popis souboru: application/xml

Přístupová URL adresa: https://www.sciencedirect.com/science/article/abs/pii/S0747717199902912
https://dialnet.unirioja.es/servlet/articulo?codigo=701508
https://dblp.uni-trier.de/db/journals/jsc/jsc29.html#Prosper00
https://www.sciencedirect.com/science/article/pii/S0747717199902912

MacMahon's Partition Analysis VI: A New Reduction Algorithm: MacMahon's partition analysis. VI: A new reduction algorithm

Autoři: Axel Riese Peter Paule George E. Andrews

Zdroj: Annals of Combinatorics. 5:251-270

Témata: Combinatorial aspects of partitions of integers, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Exact enumeration problems, generating functions, Analytic theory of partitions, 0102 computer and information sciences, 0101 mathematics, Symbolic computation and algebraic computation, magic squares, computer algebra, 01 natural sciences, partition analysis

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1756473
https://doi.org/10.1007/s00026-001-8011-y
https://core.ac.uk/display/102105322
https://link.springer.com/article/10.1007/s00026-001-8011-y

Nested derivatives: a simple method for computing series expansions of inverse functions

Autoři: Diego Dominici

Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 58, Pp 3699-3715 (2003)

Témata: 30B10 (Primary) 30D10, 33E20 (Secondary), Mathematics - Classical Analysis and ODEs, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Software, source code, etc. for problems pertaining to sequences, series, summability, 0101 mathematics, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), 01 natural sciences, Mathematics

Popis souboru: application/xml

Přístupová URL adresa: http://downloads.hindawi.com/journals/ijmms/2003/457271.pdf
http://arxiv.org/abs/math/0501052
https://doaj.org/article/d9de957ea1964415b1c3d7a6818f1cb9
http://ui.adsabs.harvard.edu/abs/2005math......1052D/abstract
https://www.hindawi.com/journals/ijmms/2003/457271/
http://www.emis.de/journals/HOA/IJMMS/2003/583699.pdf
https://downloads.hindawi.com/journals/ijmms/2003/457271.pdf
http://downloads.hindawi.com/journals/ijmms/2003/457271.pdf

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

Autoři: Jie Li Bao-Yin Zhang

Zdroj: Discrete Mathematics. 268:273-286

Témata: 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

Popis souboru: application/xml

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

Autoři: Bao-Yin Zhang

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Toward Symbolic Integration of Elliptic Integrals: Toward symbolic integration of elliptic integrals

Autoři: B. C. Carlson

Zdroj: Journal of Symbolic Computation. 28:739-753

Témata: Computational Mathematics, Computation of special functions and constants, construction of tables, Algebra and Number Theory, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), computation of special functions, Elliptic integrals as hypergeometric functions, 0101 mathematics, Symbolic computation and algebraic computation, elliptic integrals, 01 natural sciences, symbolic integration

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1423187
https://doi.org/10.1006/jsco.1999.0336

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

Autoři: Ioana Dumitriu Gene Shuman Alan Edelman

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

Témata: 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

Popis souboru: application/xml

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

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

Autoři: Doron Zeilberger

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Computerized deconstruction: Computerized deconstruction.

Autoři: Doron Zeilberger

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

Témata: 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

Popis souboru: application/xml

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

A Non-Automatic (!) Application of Gosper's Algorithm Evaluates a Determinant from Tiling Enumeration: A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration

Autoři: Ciucu, M. Krattenthaler, C.

Zdroj: Rocky Mountain J. Math. 32, no. 2 (2002), 589-607

Témata: Generalized hypergeometric series, \({}_pF_q\), 05A15 (Primary) 05A16 05A17 05A19 05B45 33C20 52C20 (Secondary), Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), tiling enumeration, Exact enumeration problems, generating functions, determinants, Determinants, permanents, traces, other special matrix functions, 0102 computer and information sciences, 52C20, 33C20, Tilings in \(2\) dimensions (aspects of discrete geometry), 01 natural sciences, 05A19, 05A17, 05A16, Mathematics - Classical Analysis and ODEs, Gosper's algorithm, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, 05A15, 05B45

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: http://arxiv.org/abs/math/0011047
https://dialnet.unirioja.es/servlet/articulo?codigo=681230
https://www.mat.univie.ac.at/~kratt/artikel/pentagon.pdf
https://projecteuclid.org/download/pdf_1/euclid.rmjm/1181070089
http://ui.adsabs.harvard.edu/abs/2000math.....11047C/abstract
http://www.mat.univie.ac.at/~kratt/artikel/pentagon.pdf
https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-32/issue-2/A-Non-Automatic--Application-of-Gospers-Algorithm-Evaluates-a/10.1216/rmjm/1030539688.short
http://projecteuclid.org/euclid.rmjm/1181070089