Search Results - "computation of special functions"

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

File Description: application/xml

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

Computation of the reverse generalized Bessel polynomials and their zeros

Authors: Dunster, T. Mark Gil Gómez, Amparo Ruiz Antolín, Diego et al.

Contributors: Dunster, T. Mark Gil Gómez, Amparo Ruiz Antolín, Diego et al.

Source: Computational and Mathematical Methods 2021, 3, 6, e1198 ; 21th International Conference Computational and Mathematical Methods in Science and Engineering (CMMSE 2021) (Online)

Subject Terms: Computation of special functions, Numerical approximations, Reverse Bessel polynomials

Relation: https://doi.org/10.1002/cmm4.1198; https://hdl.handle.net/10902/23903

Availability: https://hdl.handle.net/10902/23903
https://doi.org/10.1002/cmm4.1198

On Nonoscillating Integrals for Computing Inhomogeneous Airy Functions

Authors: Gil, Amparo Segura, Javier Temme, Nico M.

Source: Mathematics of Computation, 2001 Jul 01. 70(235), 1183-1194.

Access URL: https://www.jstor.org/stable/2698806

Efficient computation of Laguerre polynomials

Authors: Nico M. Temme Amparo Gil Javier Segura et al.

Contributors: Nico M. Temme Amparo Gil Javier Segura et al.

Source: Computer Physics Communications Volume 210, January 2017, Pages 124–131
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)

Subject Terms: FOS: Computer and information sciences, 2. Zero hunger, recurrence relations, Numerical Analysis (math.NA), asymptotic expansions, 01 natural sciences, 3. Good health, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computation of special functions and constants, construction of tables, computational algorithm, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Laguerre polynomials, Computer Science - Mathematical Software, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Mathematics - Numerical Analysis, Numerical approximation and evaluation of special functions, 0101 mathematics, Mathematical Software (cs.MS)

File Description: application/xml

Access URL: https://ir.cwi.nl/pub/25208/1-s2.0-S0010465516302727-main.pdf
http://arxiv.org/abs/1609.00829
http://hdl.handle.net/10902/11339
https://zbmath.org/6819845
https://doi.org/10.1016/j.cpc.2016.09.002
https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A25208
https://repositorio.unican.es/xmlui/handle/10902/11339
https://ir.cwi.nl/pub/25208/1-s2.0-S0010465516302727-main.pdf
http://ui.adsabs.harvard.edu/abs/2017CoPhC.210..124G/abstract
https://arxiv.org/pdf/1609.00829.pdf
https://data.mendeley.com/datasets/3jkk659cn8/1
https://hdl.handle.net/10902/11339

Branch Cuts of Stokes Wave on Deep Water. Part I: Numerical Solution and Padé Approximation: Branch cuts of Stokes wave on deep water. I: Numerical solution and Padé approximation

Authors: Sergey A. Dyachenko A. O. Korotkevich Pavel M. Lushnikov

Source: Studies in Applied Mathematics. 137:419-472

Subject Terms: Bifurcations in context of PDEs, 2. Zero hunger, Water waves, gravity waves, dispersion and scattering, nonlinear interaction, branch points, Fluid Dynamics (physics.flu-dyn), FOS: Physical sciences, Free-surface potential flows for incompressible inviscid fluids, Physics - Fluid Dynamics, Computational Physics (physics.comp-ph), Euler equations, 01 natural sciences, Physics - Atmospheric and Oceanic Physics, Computation of special functions and constants, construction of tables, infinite depth, Atmospheric and Oceanic Physics (physics.ao-ph), 0103 physical sciences, Free boundary problems for PDEs, free surface, Padé approximation, Physics - Computational Physics, Stokes wave

File Description: application/xml

Access URL: https://rss.onlinelibrary.wiley.com/doi/am-pdf/10.1111/sapm.12128
http://arxiv.org/abs/1507.02784
https://onlinelibrary.wiley.com/doi/10.1111/sapm.12128
https://arxiv.org/pdf/1507.02784

Asymptotic expansions of the complete elliptic integrals about unitary modulus

Authors: Riccardi, Giorgio VELLUCCI, PIERLUIGI DE BERNARDIS, ENRICO

Source: Communications in Applied and Industrial Mathematics e-490 (2014): 1–12. doi:10.1685/journal.caim.490
info:cnr-pdr/source/autori:RICCARDI, Giorgio; VELLUCCI, Pierluigi; DE BERNARDIS, Enrico/titolo:Asymptotic expansions of the complete elliptic integrals about unitary modulus/doi:10.1685%2Fjournal.caim.490/rivista:Communications in Applied and Industrial Mathematics/anno:2014/pagina_da:1/pagina_a:12/intervallo_pagine:1–12/volume:e-490

Subject Terms: complete elliptic integrals, asymptotic expansions, computation of special functions, computation of special functions, complete elliptic integrals, asymptotic expansions

Access URL: https://iris.uniroma3.it/handle/11590/321955
http://caim.simai.eu/index.php/caim/article/view/490/
https://hdl.handle.net/20.500.14243/304307
https://doi.org/10.1685/journal.caim.490
https://hdl.handle.net/11590/321955
https://hdl.handle.net/11591/199190

Algorithms and codes for the Macdonald function: recent progress and comparisons: Algorithms and codes for the Macdonald function: Recent progress and comparisons.

Authors: J. M. Rappoport Bruce R. Fabijonas Daniel W. Lozier

Source: Journal of Computational and Applied Mathematics. 161:179-192

Subject Terms: Bessel functions, Computational Mathematics, Computation of special functions and constants, construction of tables, Applied Mathematics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Special integral transforms (Legendre, Hilbert, etc.), Numerical approximation and evaluation of special functions, 0101 mathematics, Macdonald functions, 01 natural sciences, Numerical methods for integral transforms, Computation of special functions, Kontorovich-Lebedev integral transform

File Description: application/xml

Access URL: https://zbmath.org/2009276
https://doi.org/10.1016/s0377-0427(03)00596-x
http://ui.adsabs.harvard.edu/abs/2003JCoAM.161..179F/abstract
https://www.sciencedirect.com/science/article/pii/S037704270300596X

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

File Description: application/xml

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

Computing Complex Airy Functions by Numerical Quadrature: Computing complex Airy functions by numerical quadrature

Authors: Nico M. Temme Amparo Gil Javier Segura

Source: Numerical Algorithms. 30:11-23

Subject Terms: Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Computation of special functions and constants, construction of tables, Airy functions, numerical computation of special functions, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Numerical approximation and evaluation of special functions, Approximation in the complex plane, Numerical quadrature and cubature formulas, numerical quadrature

File Description: application/xml

Locating and computing in parallel all the simple roots of special functions using PVM

Authors: Vassilis P. Plagianakos N.K. Nousis Michael N. Vrahatis

Source: Journal of Computational and Applied Mathematics. 133:545-554

Subject Terms: construction of tables of special functions, roots of a system of equations, Kronecker-Picard theory, Computing simple roots, bisection methods, Parallel and distributed algorithms, 01 natural sciences, zero isolation, Complexity and performance of numerical algorithms, Special functions, parallel and distributed algorithms, Topological degree theory, 0101 mathematics, Elbert's conjecture, Bisection method, Computation of special functions, Degree theory for nonlinear operators, Applied Mathematics, Parallel virtual machine, Parallel numerical computation, Zero isolation, Construction of tables of special functions, Bessel functions, special functions, Computational Mathematics, Computation of special functions and constants, construction of tables, topological degree theory, computing simple roots, computation of special functions, Numerical computation of solutions to single equations, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Degree, winding number, Kronecker–Picard theory, parallel virtual machine

File Description: application/xml

Access URL: https://dialnet.unirioja.es/servlet/articulo?codigo=725319
https://www.sciencedirect.com/science/article/pii/S0377042700006750
http://www.math.upatras.gr/~vrahatis/papers/journals/PlagianakosNV01_J_COMPUT_APPL_MATH_133_pp545-554_2001.pdf
http://ui.adsabs.harvard.edu/abs/2001JCoAM.133..545P/abstract
https://www.math.upatras.gr/~vpp/pdf/a-1.pdf

The asymptotic behaviour of algebraic approximants

Authors: Yves Tourigny P. G. Drazin

Source: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. 456:1117-1137

Subject Terms: Approximation by rational functions, asymptotic analysis, Computation of special functions and constants, construction of tables, algebraic approximant, computation of special functions, 0103 physical sciences, Hermite-Padé approximation, series summation, 0101 mathematics, Padé approximation, 01 natural sciences, Power series (including lacunary series) in one complex variable

File Description: application/xml

Access URL: https://ui.adsabs.harvard.edu/abs/2000RSPSA.456.1117T/abstract
https://royalsocietypublishing.org/doi/10.1098/rspa.2000.0554
https://www.jstor.org/stable/info/2665483
https://core.ac.uk/display/79718523

On nonoscillating integrals for computing inhomogeneous Airy functions

Authors: Amparo Gil Javier Segura Nico M. Temme

Source: Mathematics of Computation. 70:1183-1195

Subject Terms: Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Numerical Analysis (math.NA), Approximation in the complex plane, 01 natural sciences, 33C10, 41A60, 65D20, Computation of special functions and constants, construction of tables, method of steepest descent, Mathematics - Classical Analysis and ODEs, computation of special functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Mathematics - Numerical Analysis, 0101 mathematics, Scorer functions, inhomogeneous Airy functions

File Description: application/xml

Access URL: https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01268-0/S0025-5718-00-01268-0.pdf
http://arxiv.org/abs/math/0109187
http://ui.adsabs.harvard.edu/abs/2001MaCom..70.1183G/abstract
https://ir.cwi.nl/pub/1130
https://www.jstor.org/stable/info/2698806
https://www.arxiv-vanity.com/papers/math/0109187/
https://dblp.uni-trier.de/db/journals/moc/moc70.html#GilST01
https://ir.cwi.nl/pub/1130/1130D.pdf

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

Authors: Prosper, V Prosper, V.

Contributors: Prosper, V Prosper, V.

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

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

Authors: Harald Böing Wolfram Koepf

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

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

Authors: B. C. Carlson

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

Subject Terms: 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

File Description: application/xml

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

Computing with Differential-difference Operators: Computing with differential-difference operators

Authors: Charles F. Dunkl

Source: Journal of Symbolic Computation. 28:819-826

Subject Terms: Dunkl operators, Algebra and Number Theory, abelian reflection groups, Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.), Connections of hypergeometric functions with groups and algebras, and related topics, Symbolic computation and algebraic computation, 01 natural sciences, polynomial arithmetic, 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, differential-difference operators, harmonic polynomials, 0101 mathematics

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0747717197903412
https://core.ac.uk/display/82520320
https://dblp.uni-trier.de/db/journals/jsc/jsc28.html#Dunkl99

Convergence Acceleration of Taylor Sections by Convolution: Convergence acceleration of Taylor sections by convolution

Authors: Jürgen Müller

Source: Constructive Approximation. 15:523-536

Subject Terms: Computation of special functions and constants, construction of tables, Hadamard product, Research exposition (monographs, survey articles) pertaining to functions of a complex variable, computation of special functions, convolution, Rate of convergence, degree of approximation, convergence acceleration, 0101 mathematics, Approximation in the complex plane, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1398360
https://doi.org/10.1007/s003659900120
https://link.springer.com/content/pdf/10.1007%2Fs003659900120.pdf
https://link.springer.com/article/10.1007/s003659900120

A quick algorithms of high precision on the exponential and logarithmic functions

Authors: Meng Yongjuan Yu Changfeng Xu Jin

Source: 2011 IEEE 2nd International Conference on Computing, Control and Industrial Engineering. :159-162

Subject Terms: Computation of special functions and constants, construction of tables, Complexity and performance of numerical algorithms, fast algorithms, Elementary functions, computational complexities, exponential and logarithm functions, high precision, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Exponential and trigonometric functions

File Description: application/xml

Access URL: https://zbmath.org/1640322
https://ieeexplore.ieee.org/document/6007982/

Smoothing of Stokes's discontinuity for the generalized Bessel function. II

Authors: Yuqiu Zhao Roderick Wong

Source: The Selected Works of Roderick S C Wong ISBN: 9789814656047

Subject Terms: Computation of special functions and constants, construction of tables, asymptotic expansion, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), generalized Bessel function, steepest-descent method, generalized Bessel functions, Stokes' phenomenon, Stokes's phenomenon, hyperasymptotics, Bessel and Airy functions, cylinder functions, \({}_0F_1\), 0101 mathematics, asymptotic expansions, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1385106
https://doi.org/10.1098/rspa.1999.0440
https://ui.adsabs.harvard.edu/abs/1999RSPSA.455.1381W/abstract
https://www.jstor.org/stable/info/53376
https://rspa.royalsocietypublishing.org/content/455/1984/1381
https://royalsocietypublishing.org/doi/10.1098/rspa.1999.0365

A Few Results on Table-Based Methods: A few results on table-based methods

Authors: Jean-Michel Muller

Source: Developments in Reliable Computing ISBN: 9789048153503

Subject Terms: table-based methods, Computation of special functions and constants, construction of tables, multipartite table method, function evaluation

File Description: application/xml

Access URL: https://hal-lara.archives-ouvertes.fr/hal-02101969/file/RR1998-46.pdf
https://zbmath.org/1421490
https://doi.org/10.1023/a:1009984523264
https://link.springer.com/content/pdf/10.1007%2F978-94-017-1247-7_22.pdf
https://dblp.uni-trier.de/db/journals/rc/rc5.html#Muller99
https://rd.springer.com/chapter/10.1007/978-94-017-1247-7_22
https://link.springer.com/article/10.1023%2FA%3A1009984523264