A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane

Authors: Dunster, T.M., Gil Gómez, Amparo, Ruiz Antolín, Diego, Segura Sala, José Javier

Contributors: Universidad de Cantabria

Source: BIT numerical mathematics, 2025, 65(2), 20
UCrea Repositorio Abierto de la Universidad de Cantabria
Universidad de Cantabria (UC)

Subject Terms: parabolic cylinder functions, Parabolic cylinder functions, Qualitative theory for ordinary differential equations, Complex zeros, complex zeros, fixed point methods, Numerical Analysis (math.NA), Approximation in the complex plane, Matlab software, Fixed point methods, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Numerical computation of solutions to single equations, Mathematics - Numerical Analysis, Numerical approximation and evaluation of special functions, 33B15, 33C15, 65D20

File Description: application/xml

Access URL: http://arxiv.org/abs/2412.13085
https://hdl.handle.net/10902/36372
https://zbmath.org/8029954
https://doi.org/10.1007/s10543-025-01065-w

On the variable-order fractional derivatives with respect to another function

Authors: Almeida, Ricardo

Source: Aequationes mathematicae. 99:805-822

Subject Terms: Fractional derivatives and integrals, expansion formulas, 0103 physical sciences, Numerical approximation and evaluation of special functions, fractional calculus, 0101 mathematics, variable-order fractional operators, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/8032556
https://doi.org/10.1007/s00010-024-01082-0

Extensions of quadratic transformation identities for hypergeometric functions

Authors: Xiao-Yan Ma, Song-liang Qiu, Yu-Ming Chu

Source: Mathematical Inequalities & Applications. :1391-1423

Subject Terms: Classical hypergeometric functions, \({}_2F_1\), Zero-balanced hypergeometric function, quadratic transformation, Numerical approximation and evaluation of special functions, 0101 mathematics, 01 natural sciences, generalized Grötzsch ring function

File Description: application/xml

Access URL: http://files.ele-math.com/abstracts/mia-23-101-abs.pdf
https://zbmath.org/7285822
https://doi.org/10.7153/mia-2020-23-101

Efficient computation of Laguerre polynomials

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

Contributors: Universidad de Cantabria

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

Fast conversion algorithms for orthogonal polynomials

Authors: Alin Bostan, Éric Schost, Bruno Salvy

Source: Linear Algebra and its Applications. 432:249-258

Subject Terms: Computer Science - Symbolic Computation, FOS: Computer and information sciences, Basis conversion, fast algorithms, Orthogonal polynomials, Analysis of algorithms and problem complexity, Numerical methods for trigonometric approximation and interpolation, conversion algorithms, 0102 computer and information sciences, transposed algorithms, Symbolic Computation (cs.SC), Transposed algorithms, 01 natural sciences, Fast algorithms, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Complexity and performance of numerical algorithms, Discrete Mathematics and Combinatorics, Analysis of algorithms, Numerical approximation and evaluation of special functions, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, basis conversion, orthogonal polynomials, Numerical Analysis, Algebra and Number Theory, Computation of special functions and constants, construction of tables, Geometry and Topology, complexity

File Description: application/xml

Access URL: http://arxiv.org/abs/0804.2373
https://zbmath.org/5650034
https://doi.org/10.1016/j.laa.2009.08.002
https://arxiv.org/abs/0804.2373
https://arxiv.org/pdf/0804.2373.pdf
https://hal.archives-ouvertes.fr/inria-00273508
https://core.ac.uk/display/81116146
http://www.csd.uwo.ca/~eschost/publications/BoSaSc08b-r1.pdf
https://www.sciencedirect.com/science/article/pii/S002437950900408X

Numerical Kähler-Einstein Metric on the Third del Pezzo: Numerical Kähler-Einstein metric on the third del Pezzo

Authors: J. Kantor, Christopher P. Herzog, Charles F. Doran, Matthew Headrick, Toby Wiseman

Source: Communications in Mathematical Physics. 282:357-393

Subject Terms: High Energy Physics - Theory, Mathematics - Differential Geometry, Kähler-Einstein manifolds, numerical approximations, FOS: Physical sciences, 16. Peace & justice, 01 natural sciences, Kähler-Einstein metrics, High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), Ricci flow, 0103 physical sciences, FOS: Mathematics, Numerical approximation and evaluation of special functions, 0101 mathematics, Toric varieties, Newton polyhedra, Okounkov bodies, Geometric evolution equations (mean curvature flow, Ricci flow, etc.), toric varieties

File Description: application/xml

Access URL: http://arxiv.org/pdf/hep-th/0703057
http://arxiv.org/abs/hep-th/0703057
https://zbmath.org/5488671
https://doi.org/10.1007/s00220-008-0558-6
http://insti.physics.sunysb.edu/~cpherzog/dP3/dp3metric.pdf
https://link.springer.com/article/10.1007%2Fs00220-008-0558-6
http://ui.adsabs.harvard.edu/abs/2008CMaPh.282..357D/abstract
https://www.arxiv-vanity.com/papers/hep-th/0703057/
http://export.arxiv.org/pdf/hep-th/0703057
https://arxiv.org/pdf/hep-th/0703057.pdf
https://arxiv.org/abs/hep-th/0703057

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

File Description: application/xml

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

WAVELET DEFORMATION ANALYSIS FOR SPHERICAL BODIES: Wavelet deformation analysis for spherical bodies

Authors: Freeden, Willi, Michel, Volker

Source: International Journal of Wavelets, Multiresolution and Information Processing. :523-558

Subject Terms: msc:42C40, msc:74B05, Dirichlet's and Neumann's boundary value problem, msc:86A20, msc:33F05, Mehrskalenanalyse, Nontrigonometric harmonic analysis involving wavelets and other special systems, Elastische Deformation, 01 natural sciences, Potentials, prospecting, spherical multiscale deformation analysis, Navier scaling functions and wavelets, Neumann-Problem, Dirichlet-Problem, Classical linear elasticity, Cauchy-Navier equation, Wavelet-Analyse, Skalierungsfunktion, ddc:510, Cauchy-Navier-Gleichung, Numerical approximation and evaluation of special functions, 0101 mathematics, Kugel

File Description: application/xml; application/pdf

Access URL: https://kluedo.ub.uni-kl.de/files/1612/gelber_Report9.pdf
https://zbmath.org/2244218
https://doi.org/10.1142/s0219691305001007
https://www.worldscientific.com/doi/abs/10.1142/S0219691305001007
https://kluedo.ub.uni-kl.de/frontdoor/index/index/year/2005/docId/1612
http://dblp.uni-trier.de/db/journals/ijwmip/ijwmip3.html#FreedenM05
https://dblp.uni-trier.de/db/journals/ijwmip/ijwmip3.html#FreedenM05
https://kluedo.ub.uni-kl.de/files/1612/gelber_Report9.pdf
https://kluedo.ub.rptu.de/frontdoor/index/index/docId/1612

A new friendly method of computing prolate spheroidal wave functions and wavelets

Authors: T. Soleski, Gilbert G. Walter

Source: Applied and Computational Harmonic Analysis. 19:432-443

Subject Terms: Integral operators, numerical examples, Eigenvalue problems for integral equations, Lamé, Mathieu, and spheroidal wave functions, Applied Mathematics, Sampling theory, matrix operator, eigenfunctions, Prolate spheroidal wave functions, Numerical methods for integral equations, integral operator, wavelets, 01 natural sciences, Computation of special functions and constants, construction of tables, Numerical methods for wavelets, eigenvalue problem, Numerical approximation and evaluation of special functions, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/2244676
https://doi.org/10.1016/j.acha.2005.04.001
https://www.sciencedirect.com/science/article/pii/S1063520305000552
http://core.ac.uk/display/22948965
https://www.sciencedirect.com/science/article/abs/pii/S1063520305000552

Calculation of generalized elliptic type integrals using the binomial expansion theorem

Authors: Mamedov, BA, Tapramaz, R, Merdan, Z

Contributors: Ondokuz Mayıs Üniversitesi

Source: Applied Mathematics and Computation. 168:333-341

Subject Terms: numerical examples, convergence, radiation field, elliptic-type integrals, binomial coefficients, 01 natural sciences, Computation of special functions and constants, construction of tables, Elliptic functions and integrals, Elliptic-type integrals, Radiation field, 0103 physical sciences, Binomial coefficients, Numerical approximation and evaluation of special functions, 0101 mathematics

File Description: application/xml

Access URL: https://avesis.gazi.edu.tr/publication/details/67bfcc34-7856-460a-bfaf-703f384d4500/oai

Numerical Quadrature Computation of the Macdonald Function for Complex Orders: Numerical quadrature computation of the Macdonald function for complex orders

Authors: Walter Gautschi

Source: BIT Numerical Mathematics. 45:593-603

Subject Terms: Matlab routine, numerical examples, Computation of special functions and constants, construction of tables, Packaged methods for numerical algorithms, Gaussian quadrature formulae, modified Bessel function, complex orders, Gauss-Legendre quadrature, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Numerical approximation and evaluation of special functions, 0101 mathematics, Software, source code, etc. for problems pertaining to special functions, 01 natural sciences

File Description: application/xml

Access URL: https://rd.springer.com/article/10.1007/s10543-005-0020-5
https://link.springer.com/content/pdf/10.1007/s10543-005-0020-5.pdf
https://link.springer.com/article/10.1007/s10543-005-0020-5

Effective solution of the problem of the optimal stability polynomial

Authors: Andrei Bogatyrev

Source: Sbornik: Mathematics. 196:959-981

Subject Terms: Computation of special functions and constants, construction of tables, Exponential function, polynomial approximation, Numerical approximation and evaluation of special functions, 0101 mathematics, 01 natural sciences, Exponential and trigonometric functions

File Description: application/xml

Access URL: http://ui.adsabs.harvard.edu/abs/2005SbMat.196..959B/abstract
https://stacks.iop.org/1064-5616/196/i=7/a=A02?key=crossref.6c5d7b8f4b8862d742f3ebcf5cd5ec5a

Least squares fitting Gaussian type curve

Authors: Dragan Jukić, Rudolf Scitovski

Source: Applied Mathematics and Computation. 167:286-298

Subject Terms: Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals), 02 engineering and technology, nonlinear least squares, weighted least squares fitting, 01 natural sciences, least squares estimate, Computation of special functions and constants, construction of tables, Gaussian function, existence problem, Numerical smoothing, curve fitting, 0202 electrical engineering, electronic engineering, information engineering, Numerical approximation and evaluation of special functions, 0101 mathematics, numerical experiments

File Description: application/xml

Access URL: https://www.bib.irb.hr/225043
https://zbmath.org/2220596
https://doi.org/10.1016/j.amc.2004.06.084
https://www.sciencedirect.com/science/article/pii/S0096300304004928
https://dblp.uni-trier.de/db/journals/amc/amc167.html#JukicS05
http://www.sciencedirect.com/science/article/pii/S0096300304004928

The computation of orthogonal rational functions on an interval

Authors: J. Van Deun, Adhemar Bultheel

Source: Journal of Computational and Applied Mathematics. 179:355-373

Subject Terms: numerical examples, Computational Mathematics, Computation of special functions and constants, construction of tables, recurrence coefficients, Quadrature, Applied Mathematics, Orthogonal rational functions, Other special orthogonal polynomials and functions, error bounds, Numerical approximation and evaluation of special functions, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2173205
https://doi.org/10.1016/j.cam.2004.09.050
https://www.sciencedirect.com/science/article/pii/S0377042704004595
https://www.sciencedirect.com/science/article/abs/pii/S0377042704004595
https://core.ac.uk/display/82499393
http://ui.adsabs.harvard.edu/abs/2005JCoAM.179..355V/abstract

Combinatorial and hypergeometric identities via the Legendre polynomials––A computational approach: Combinatorial and hypergeometric identities via the Legendre polynomials -- a computational approach

Authors: Gi-Sang Cheon, Moawwad El-Mikkawy

Source: Applied Mathematics and Computation. 166:181-195

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Computation of special functions and constants, construction of tables, Orthogonal polynomials, MAPLE, Legendre polynomials, Numerical approximation and evaluation of special functions, combinatorial and hypergeometric identities, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Hypergeometric series

File Description: application/xml

Access URL: https://zbmath.org/2192379
https://doi.org/10.1016/j.amc.2004.04.066
http://www.sciencedirect.com/science/article/pii/S0096300304004291
https://dblp.uni-trier.de/db/journals/amc/amc166.html#El-MikkawyC05
https://www.sciencedirect.com/science/article/pii/S0096300304004291

Computation of the logarithm of Bessel functions of complex argument

Authors: Edward J. Rothwell

Source: Communications in Numerical Methods in Engineering. 21:597-605

Subject Terms: boundary value problems, eigenvalues, eigenfunctions, 02 engineering and technology, numerical results, algorithms, 01 natural sciences, logarithm of Bessel functions, Computation of special functions and constants, construction of tables, electromagnetic scattering, 0202 electrical engineering, electronic engineering, information engineering, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Numerical approximation and evaluation of special functions, 0101 mathematics, Diffraction, scattering

File Description: application/xml

Access URL: https://zbmath.org/2225434
https://doi.org/10.1002/cnm.776
https://onlinelibrary.wiley.com/doi/10.1002/cnm.776

New analytical approximations for the Mathieu functions

Authors: K. Z. Nobrega, Cesar Augusto Dartora, Hugo E. Hernandez-Figueroa

Source: Applied Mathematics and Computation. 165:447-458

Subject Terms: Computation of special functions and constants, construction of tables, Lamé, Mathieu, and spheroidal wave functions, 0103 physical sciences, Numerical approximation and evaluation of special functions, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://www.sciencedirect.com/science/article/pii/S0096300304003935
https://dblp.uni-trier.de/db/journals/amc/amc165.html#DartoraNH05
https://doi.org/10.1016/j.amc.2004.06.023
https://www.sciencedirect.com/science/article/pii/S0096300304003935

Orthogonal polynomials (in Matlab)

Authors: GautschiWalter

Source: Journal of Computational and Applied Mathematics. 178:215-234

Subject Terms: Orthogonal polynomials, discretization methods, Applied Mathematics, Recurrence relations, package, 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, Packaged methods for numerical algorithms, Numerical approximation and evaluation of special functions, 0101 mathematics, moment-based methods, Matlab

File Description: application/xml

Access URL: https://zbmath.org/2157670
https://doi.org/10.1016/j.cam.2004.03.029
http://ui.adsabs.harvard.edu/abs/2005JCoAM.178..215G/abstract
http://ecaaser3.ecaa.ntu.edu.tw/weifang/ebook/matlab/Orthogonal%20polynomials%20(in%20Matlab).pdf
https://www.cs.purdue.edu/homes/wxg/OPmatlab.pdf
https://www.sciencedirect.com/science/article/pii/S0377042704003760
https://core.ac.uk/display/82161067
https://www.sciencedirect.com/science/article/abs/pii/S0377042704003760
https://dl.acm.org/doi/10.5555/1075051.1716686

On quadrature of Bessel transformations

Authors: Shuhuang Xiang

Source: Journal of Computational and Applied Mathematics. 177:231-239

Subject Terms: numerical examples, Applied Mathematics, Integral transforms of special functions, 01 natural sciences, Bessel functions, Computational Mathematics, Computation of special functions and constants, construction of tables, integral transformations of highly oscillatory functions, quadrature, Bessel and Airy functions, cylinder functions, \({}_0F_1\), Numerical approximation and evaluation of special functions, 0101 mathematics, Filon-type method, Numerical methods for integral transforms

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042704004339
http://ui.adsabs.harvard.edu/abs/2005JCoAM.177..231X/abstract
https://www.sciencedirect.com/science/article/pii/S0377042704004339
https://core.ac.uk/display/82541681

A new Sigma approach to multi-summation

Authors: Carsten Schneider

Source: Advances in Applied Mathematics. 34:740-767

Subject Terms: Applied Mathematics, 0102 computer and information sciences, Numerical approximation and evaluation of special functions, Gröbner bases, other bases for ideals and modules (e.g., Janet and border bases), 0101 mathematics, Symbolic computation and algebraic computation, Orthogonal polynomials (combinatorics), 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2190414
https://doi.org/10.1016/j.aam.2004.07.009
https://www.sciencedirect.com/science/article/pii/S0196885804001459
https://dblp.uni-trier.de/db/journals/aam/aam34.html#Schneider05
http://www.ricam.oeaw.ac.at/Groebner-Bases-Bibliography/gbbib_files/publication_680.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0196885804001459
https://www.ricam.oeaw.ac.at/Groebner-Bases-Bibliography/gbbib_files/publication_680.pdf
https://core.ac.uk/display/24464187