Dougall’s 5F4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_5F_4$$\end{document} sum and the WZ algorithm

Συγγραφείς: Guillera, Jesús^{Aff1, cor1}

Πηγή: The Ramanujan Journal: An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan. 46(3):667-675

Mahler measure and the WZ algorithm

Συγγραφείς: Guillera, Jesús, Rogers, Mathew

Πηγή: Proceedings of the American Mathematical Society. 143:2873-2886

Θεματικοί όροι: Generalized hypergeometric series, \({}_pF_q\), Mathematics - Number Theory, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Mahler measure, FOS: Mathematics, Number Theory (math.NT), 33C20, 33F10, 19F27, 0101 mathematics, WZ algorithm, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/1006.1654
http://arxiv.org/abs/1006.1654

An Ansatz for the asymptotics of hypergeometric multisums

Συγγραφείς: Stavros Garoufalidis

Πηγή: Advances in Applied Mathematics. 41:423-451

Θεματικοί όροι: Additive K-theory, Holonomic functions, Hadamard product, Laplace transform, Polytopes, Transseries, G-functions, \(G\)-function, singular points, WZ algorithm, 01 natural sciences, Diagonals of rational functions, Other hypergeometric functions and integrals in several variables, Mathematics - Algebraic Geometry, Stirling formula, Regulators, FOS: Mathematics, Mathematics - Combinatorics, 0101 mathematics, Algebraic Geometry (math.AG), Asymptotics and summation methods for ordinary differential equations in the complex domain, Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms, asymptotic expansion, Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions), Picard-Fuchs differential equation, Applied Mathematics, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), terminating multiple hypergeometric series, Regular holonomic functions, Bethe ansatz, Balanced hypergeometric terms, Asymptotic enumeration, balanced term, Asymptotic expansions, Algebraic combinatorics, Newton polytope, Combinatorics (math.CO), Singularities, Newton polytopes

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/0706.0722
https://zbmath.org/5355932
https://doi.org/10.1016/j.aam.2008.02.002

TheC–polynomial of a knot: The \(C\)-polynomial of a knot

Συγγραφείς: Garoufalidis, Stavros, Sun, Xinyu

Πηγή: Algebr. Geom. Topol. 6, no. 4 (2006), 1623-1653

Θεματικοί όροι: Topology of general \(3\)-manifolds, characteristic varieties, colored Jones function, Geometric Topology (math.GT), cyclotomic function, WZ algorithm, Invariants of knots and \(3\)-manifolds, creative telescoping, 01 natural sciences, 57N10, twist knots, Mathematics - Geometric Topology, non-commutative \(A\)-polynomial, holonomic functions, 57M25, Gosper's algorithm, FOS: Mathematics, Knots and links in the \(3\)-sphere, Mathematics - Combinatorics, 57N10, 57M25, Combinatorics (math.CO), $A$-polynomial, $C$-polynomial, 0101 mathematics

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://msp.org/agt/2006/6-4/agt-v6-n4-p02-s.pdf
http://arxiv.org/abs/math/0504305
https://zbmath.org/5118572
https://doi.org/10.2140/agt.2006.6.1623
https://projecteuclid.org/euclid.agt/1513796600

The colored Jones function is q-holonomic: The colored Jones function is \(q\)-holonomic

Συγγραφείς: Garoufalidis, Stavros, Le, Thang T Q

Πηγή: Geom. Topol. 9, no. 3 (2005), 1253-1293

Θεματικοί όροι: Knots, Topology of general \(3\)-manifolds, knots, multisums, Geometric Topology (math.GT), D-modules, Invariants of knots and \(3\)-manifolds, WZ algorithm, 01 natural sciences, Jones polynomial, Jones polynomials, 57N10, Mathematics - Geometric Topology, $D$–modules, 57M25, holonomic functions, Mathematics - Quantum Algebra, 0103 physical sciences, quantum invariants, FOS: Mathematics, Knots and links in the \(3\)-sphere, Quantum Algebra (math.QA), 57N10, 57M25, 0101 mathematics, hypergeometric functions

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://msp.org/gt/2005/9-3/gt-v9-n3-p03-s.pdf
http://arxiv.org/abs/math/0309214
https://projecteuclid.org/euclid.gt/1513799636

Dougall's $_5F_4$ sum and the WZ-algorithm: Dougall's \(_5F_4\) sum and the WZ algorithm

Συγγραφείς: Guillera, Jesús

Θεματικοί όροι: evaluation of constants, Generalized hypergeometric series, \({}_pF_q\), Evaluation of number-theoretic constants, Mathematics - Number Theory, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Dougall's sum, Ramanujan-type series, FOS: Mathematics, Number Theory (math.NT), WZ algorithm, 33C20, 33F10, 11Y60, generalized hypergeometric series

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1611.04385

Curious relations and identities involving the Catalan generating function and numbers

Συγγραφείς: Nkwanta, Asamoah, Tefera, Akalu

Θεματικοί όροι: Catalan number, gamma function, generating function, Riordan array, Exact enumeration problems, generating functions, WZ method, WZ algorithm, Combinatorial identities, bijective combinatorics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/6272443

A short proof for the existence of the WZ-factorisation

Συγγραφείς: Michael Kaps, Michael Schlegl

Πηγή: Parallel Computing. 4:229-232

Θεματικοί όροι: LU factorization, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, 0101 mathematics, Direct numerical methods for linear systems and matrix inversion, WZ-algorithm, parallel computation, 01 natural sciences, Factorization of matrices

Περιγραφή αρχείου: application/xml

Advantages for solving linear systems in an asynchronous environment

Συγγραφείς: HATZOPOULOS, M, MISSIRLIS, NM

Πηγή: Journal of Computational and Applied Mathematics. :331-340

Θεματικοί όροι: Analysis of algorithms and problem complexity, Applied Mathematics, parallel computers, MIMD, 0102 computer and information sciences, 02 engineering and technology, Direct numerical methods for linear systems and matrix inversion, 01 natural sciences, Computational Mathematics, Gauss-Jordan algorithm, 0202 electrical engineering, electronic engineering, information engineering, Software, source code, etc. for problems pertaining to linear algebra, asynchronous multiprocessor computer, WZ-algorithm, Gauss algorithm

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/3921814
https://doi.org/10.1016/0377-0427(85)90028-7
https://pergamos.lib.uoa.gr/uoa/dl/object/3041594

The colored Jones function is q-holonomic

Συγγραφείς: Stavros Garoufalidis, Thang T Q Lê, Zeilberger Meets Jones

Συνεισφορές: The Pennsylvania State University CiteSeerX Archives

Πηγή: http://www.msp.warwick.ac.uk/gt/2005/09/gt-2005-09-029s.pdf.

Θεματικοί όροι: Holonomic functions, Jones polynomial, Knots, WZ algorithm, quantum invariants, D–modules, multisums, hypergeometric functions

Περιγραφή αρχείου: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.2232

Διαθεσιμότητα: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.2232
http://www.msp.warwick.ac.uk/gt/2005/09/gt-2005-09-029s.pdf

Geometry & Topology Monographs Volume 7: Proceedings of the Casson Fest Pages 291–309

Συνεισφορές: The Pennsylvania State University CiteSeerX Archives

Πηγή: http://www.emis.de/journals/GT/ftp/main/m7/m7l12.pdf.

Θεματικοί όροι: D–modules, characteristic variety, de- formation variety, colored Jones function, multisums, hypergeometric func- tions, WZ algorithm. Dedicated to Andrew Casson on the occasion of his 60th

Περιγραφή αρχείου: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.525.7032; http://www.emis.de/journals/GT/ftp/main/m7/m7l12.pdf

Διαθεσιμότητα: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.525.7032
http://www.emis.de/journals/GT/ftp/main/m7/m7l12.pdf