Magomed-Kasumov, M. G. The uniform convergence of Fourier series in a system of the Sobolev orthogonal polynomials associated to ultraspherical Jacobi polynomials. (English. Russian original) Zbl 07947583 Sib. Math. J. 65, No. 6, 1343-1358 (2024); translation from Sib. Mat. Zh. 65, No. 6, 1173-1190 (2024). MSC: 42A20 42C10 42C05 33C45 46E35 × Cite Format Result Cite Review PDF Full Text: DOI
Naidenov, Nikola; Nikolov, Geno Estimates for the largest critical value of \(T_n^{(k)}\). (English) Zbl 1548.41011 Constr. Approx. 60, No. 1, 87-103 (2024). Reviewer: Andriy Prymak (Winnipeg) MSC: 41A17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sajjadi, Sayed Arsalan; Saberi Najafi, Hashem; Aminikhah, Hossein An efficient numerical method based on ultraspherical polynomials for linear weakly singular fractional Volterra integro-differential equations. (English) Zbl 07883083 Math. Methods Appl. Sci. 47, No. 12, 10293-10308 (2024). MSC: 26A33 47G20 65R10 × Cite Format Result Cite Review PDF Full Text: DOI
Dunster, T. M. Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole. (English) Zbl 1537.33010 Constr. Approx. 59, No. 2, 419-456 (2024). MSC: 33C45 34E20 34E05 34M30 41A60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nikolov, Geno Turán’s inequality for ultraspherical polynomials revisited. (English) Zbl 1536.33010 Math. Inequal. Appl. 26, No. 2, 343-349 (2023). Reviewer: Xiang-Sheng Wang (Lafayette) MSC: 33C45 42C05 33C55 26C10 26A51 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chang, Der-Chen; Chang, Shu-Cheng; Han, Yingbo; Tie, Jingzhi Yau’s conjecture on the dimension of harmonic polynomials. (English) Zbl 1528.32052 Lenhart, Suzanne (ed.) et al., Potentials and partial differential equations. The legacy of David R. Adams. Berlin: De Gruyter. Adv. Anal. Geom. 8, 1-21 (2023). MSC: 32V05 32V20 53C56 × Cite Format Result Cite Review PDF Full Text: DOI
Derevyagin, Maxim; Geronimo, Jeffrey S. Connection coefficients for ultraspherical polynomials with argument doubling and generalized bispectrality. (English) Zbl 1532.33016 J. Anal. Math. 150, No. 1, 57-81 (2023). MSC: 33C45 33C55 42C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Chunsheng Vector random fields on the probability simplex with metric-dependent covariance matrix functions. (English) Zbl 1517.60055 J. Theor. Probab. 36, No. 3, 1922-1938 (2023). MSC: 60G60 60G22 62M10 62M20 × Cite Format Result Cite Review PDF Full Text: DOI
Cheng, Lu; Xu, Kuan Solving time-dependent PDEs with the ultraspherical spectral method. (English) Zbl 07722590 J. Sci. Comput. 96, No. 3, Paper No. 70, 34 p. (2023). MSC: 65Mxx 65L04 65M12 65M15 65M20 65M70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Koornwinder, Tom H. Dual addition formulas: the case of continuous \(q\)-ultraspherical and \(q\)-Hermite polynomials. (English) Zbl 1530.33021 Ramanujan J. 61, No. 2, 425-444 (2023). MSC: 33D45 39B12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Khani, Ali; Panahi, Saeid Solving fractional differential equations by the ultraspherical integration method. (English) Zbl 1549.34032 Bol. Soc. Parana. Mat. (3) 40, Paper No. 23, 14 p. (2022). MSC: 34A08 65L20 × Cite Format Result Cite Review PDF Full Text: DOI
Singh, Yamini; Srivastava, R. An analysis of \((0, 1, 2; 0)\) polynomial interpolation including interpolation on boundary points of interval \([-1, 1]\). (English) Zbl 1538.41008 Bull. Transilv. Univ. Brașov, Ser. III, Math. Comput. Sci. 2(64), No. 1, 159-176 (2022). MSC: 41A05 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Hamzehnejad, Mehdi; Hosseini, Mohammad Mehdi; Salemi, Abbas An improved upper bound for ultraspherical coefficients. (English) Zbl 1524.41032 J. Math. Model. 10, No. 3, 421-431 (2022). MSC: 41A25 41A10 × Cite Format Result Cite Review PDF Full Text: DOI
Casarino, Valentina; Ciatti, Paolo; Martini, Alessio Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators. (English) Zbl 1505.43007 Int. Math. Res. Not. 2022, No. 12, 9209-9274 (2022). MSC: 43A85 42B15 58J50 33C55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Szabłowski, Paweł J. On the families of polynomials forming a part of the Askey-Wilson scheme and their probabilistic applications. (English) Zbl 1509.33020 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 1, Article ID 2230001, 57 p. (2022). MSC: 33D45 05A30 42C05 60E05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Abdelhakem, Mohamed; Mahmoud, Doha; Baleanu, Dumitru; El-kady, Mamdouh Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems. (English) Zbl 1494.65064 Adv. Difference Equ. 2021, Paper No. 110, 18 p. (2021). MSC: 65L60 26A33 34A08 × Cite Format Result Cite Review PDF Full Text: DOI
Ma, Z.; Ma, C. Series representations and simulations of isotropic random fields in the Euclidean space. (English) Zbl 1493.60084 Theory Probab. Math. Stat. 105, 93-111 (2021). MSC: 60G60 33C10 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Magomed-Kasumov, M. G. Approximation properties of Vallée Poussin means for special series of ultraspherical Jacobi polynomials. (English) Zbl 1484.33015 Kusraev, Anatoly G. (ed.) et al., Operator theory and differential equations. Selected papers based on the presentations at the 15th conference on order analysis and related problems of mathematical modeling, Vladikavkaz, Russia, July 15–20, 2019. Cham: Birkhäuser. Trends Math., 107-120 (2021). MSC: 33C45 41A25 42C10 × Cite Format Result Cite Review PDF Full Text: DOI
Metwally, M. S.; Shehata, S. A study of ultraspherical matrix polynomials of two variables. (English) Zbl 1468.33005 Util. Math. 115, 3-21 (2020). MSC: 33C05 15A60 33C45 33E20 × Cite Format Result Cite Review PDF
Erb, Wolfgang Weak limits for weighted means of orthogonal polynomials. (English) Zbl 1465.42025 J. Spectr. Theory 10, No. 3, 787-808 (2020). Reviewer: Krzysztof Stempak (Wrocław) MSC: 42C05 40G05 60B10 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fortunato, Daniel; Townsend, Alex Fast Poisson solvers for spectral methods. (English) Zbl 1466.65186 IMA J. Numer. Anal. 40, No. 3, 1994-2018 (2020). MSC: 65N30 65N22 35J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sultanakhmedov, M. S. Recurrence relations for Sobolev orthogonal polynomials. (English) Zbl 1466.42021 Probl. Anal. Issues Anal. 9(27), No. 2, 97-118 (2020). MSC: 42C05 26C05 33C47 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Srivastava, R.; Singh, Yamini A \((0; 0, 2)\) interpolation method to approximate functions via ultraspherical polynomials. (English) Zbl 1463.41006 J. Indian Math. Soc., New Ser. 87, No. 3-4, 276-288 (2020). MSC: 41A05 97N50 × Cite Format Result Cite Review PDF Full Text: DOI
Bihun, Oksana; Driver, Kathy Orthogonal sequences constructed from quasi-orthogonal ultraspherical polynomials. (English) Zbl 1458.33007 Numer. Algorithms 85, No. 2, 503-522 (2020). Reviewer: Adhemar Bultheel (Leuven) MSC: 33C50 42C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Betancor, Jorge J.; Castro, Alejandro J.; Fariña, Juan C.; Rodríguez-Mesa, L. Discrete harmonic analysis associated with ultraspherical expansions. (English) Zbl 1472.39008 Potential Anal. 53, No. 2, 523-563 (2020). Reviewer: Raghib Abu-Saris (Edmonton) MSC: 39A12 39A70 39A14 42A38 42B25 42C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sharapudinov, I. I. The basis property of ultraspherical Jacobi polynomials in a weighted Lebesgue space with variable exponent. (English. Russian original) Zbl 1434.33018 Math. Notes 106, No. 4, 616-638 (2019); translation from Mat. Zametki 106, No. 4, 595-621 (2019). MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Hale, Nicholas An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type. (English) Zbl 1464.65204 IMA J. Numer. Anal. 39, No. 4, 1727-1746 (2019). MSC: 65N35 65L60 35R09 45K05 45B05 45D05 45J05 65R20 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nie, Zhihui; Ma, Chunsheng Isotropic positive definite functions on spheres generated from those in Euclidean spaces. (English) Zbl 1426.33031 Proc. Am. Math. Soc. 147, No. 7, 3047-3056 (2019). Reviewer: Chrysoula G. Kokologiannaki (Patras) MSC: 33C45 33C50 42A82 60E10 × Cite Format Result Cite Review PDF Full Text: DOI Link
AlSabi, Hashem; Griffin, James Ultraspherical moments on a set of disjoint intervals. (English) Zbl 1433.33006 Indag. Math., New Ser. 30, No. 4, 596-609 (2019). MSC: 33C47 33C05 33B15 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dai, Dan; Ismail, Mourad E. H.; Wang, Xiang-Sheng Doubly infinite Jacobi matrices revisited: resolvent and spectral measure. (English) Zbl 07003588 Adv. Math. 343, 157-192 (2019). MSC: 47B36 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Gautschi, Walter On the Ismail-Letessier-Askey monotonicity conjecture for zeros of ultraspherical polynomials. (English) Zbl 1411.33009 Nashed, M. Zuhair (ed.) et al., Frontiers in orthogonal polynomials and \(q\)-series. Papers based on the international conference, University of Central Florida, Orlando, FL, USA, May 10–12, 2015. Dedicated to Professor Mourad Ismail on his 70th birthday. Hackensack, NJ: World Scientific. Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 251-266 (2018). MSC: 33C45 65D20 × Cite Format Result Cite Review PDF Full Text: DOI
Srivastava, R.; Singh, Yamini An interpolation process on the roots of ultraspherical polynomials. (English) Zbl 1406.41003 Appl. Appl. Math. 13, No. 2, 1132-1140 (2018). MSC: 41A10 65D05 × Cite Format Result Cite Review PDF Full Text: Link
Sharapudinov, I. I.; Magomed-Kasumov, M. G. The Valleé-Poussin means for special series with respect to ultraspherical Jacobi polynomials with sticking partial sums. (English. Russian original) Zbl 1405.41004 Russ. Math. 62, No. 9, 60-71 (2018); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2018, No. 9, 68-80 (2018). MSC: 41A10 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Sharapudinov, I. I. Sobolev orthogonal polynomials generated by Jacobi and Legendre polynomials, and special series with the sticking property for their partial sums. (English. Russian original) Zbl 1416.33019 Sb. Math. 209, No. 9, 1390-1417 (2018); translation from Mat. Sb. 209, No. 9, 142-170 (2018). Reviewer: Alexei Lukashov (Saratov) MSC: 33C45 42C10 × Cite Format Result Cite Review PDF Full Text: DOI
Beatson, Rick K.; zu Castell, Wolfgang Thinplate splines on the sphere. (English) Zbl 1400.41009 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 083, 22 p. (2018). MSC: 41A15 33C45 42A82 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hale, Nicholas; Olver, Sheehan A fast and spectrally convergent algorithm for rational-order fractional integral and differential equations. (English) Zbl 1397.65124 SIAM J. Sci. Comput. 40, No. 4, A2456-A2491 (2018). MSC: 65L99 34A08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Kuan; Loureiro, Ana F. Spectral approximation of convolution operators. (English) Zbl 1396.65158 SIAM J. Sci. Comput. 40, No. 4, A2336-A2355 (2018). MSC: 65R10 44A35 42A85 47A58 33C45 41A10 65Q30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Arenas, Alberto; Ciaurri, Óscar; Labarga, Edgar A Hardy inequality for ultraspherical expansions with an application to the sphere. (English) Zbl 1387.42030 J. Fourier Anal. Appl. 24, No. 2, 416-430 (2018). MSC: 42C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ma, Chunsheng Time varying isotropic vector random fields on spheres. (English) Zbl 1408.60039 J. Theor. Probab. 30, No. 4, 1763-1785 (2017). MSC: 60G60 62M10 62M30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Slevinsky, Richard Mikael; Olver, Sheehan A fast and well-conditioned spectral method for singular integral equations. (English) Zbl 1380.65446 J. Comput. Phys. 332, 290-315 (2017). MSC: 65R20 45E99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Aldenhoven, Noud; Koelink, Erik; Román, Pablo Matrix-valued orthogonal polynomials related to the quantum analogue of \((\mathrm{SU}(2) \times \mathrm{SU}(2), \text{diag})\). (English) Zbl 1433.17013 Ramanujan J. 43, No. 2, 243-311 (2017). MSC: 17B37 33D45 33D80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krasikov, Ilia On approximation of ultraspherical polynomials in the oscillatory region. (English) Zbl 1378.33007 J. Approx. Theory 222, 143-156 (2017). Reviewer: Marcel G. de Bruin (Heemstede) MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Kapfer, Simon Symmetric powers of symmetric bilinear forms, homogeneous orthogonal polynomials on the sphere and an application to compact hyperkähler manifolds. (English) Zbl 1374.14005 Commun. Contemp. Math. 19, No. 2, Article ID 1650007, 19 p. (2017). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 14C05 15A63 33C50 32Q15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mesk, Mohammed; Zahaf, Mohammed Brahim A new characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind. (English) Zbl 1398.33005 J. Math. Anal. Appl. 448, No. 2, 1147-1162 (2017). MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Driver, Kathy; Muldoon, Martin E. Bounds for extreme zeros of quasi-orthogonal ultraspherical polynomials. (English) Zbl 1424.33023 J. Class. Anal. 9, No. 1, 69-78 (2016). MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Potts, Daniel; Tasche, Manfred Reconstruction of sparse Legendre and Gegenbauer expansions. (English) Zbl 1398.65028 BIT 56, No. 3, 1019-1043 (2016). Reviewer: Yanlai Chen (North Dartmouth) MSC: 65D20 65D05 33C45 41A45 65F15 × Cite Format Result Cite Review PDF Full Text: DOI
Driver, Kathy; Muldoon, Martin E. Zeros of quasi-orthogonal ultraspherical polynomials. (English) Zbl 1350.30008 Indag. Math., New Ser. 27, No. 4, 930-944 (2016). Reviewer: Adhemar Bultheel (Leuven) MSC: 30C10 33C45 26C10 × Cite Format Result Cite Review PDF Full Text: DOI
Kopotun, K. A.; Leviatan, D.; Prymak, A.; Shevchuk, I. A. Yet another look at positive linear operators, \(q\)-monotonicity and applications. (English) Zbl 1350.41004 J. Approx. Theory 210, 1-22 (2016). Reviewer: Vijay Gupta (New Delhi) MSC: 41A05 41A25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Arenas, A.; Ciaurri, Ó.; Labarga, E. Weighted inequalities for the Riesz potential on the sphere. (English) Zbl 1350.42020 Integral Transforms Spec. Funct. 27, No. 6, 511-522 (2016). Reviewer: Sunggeum Hong (Gwangju) MSC: 42B20 × Cite Format Result Cite Review PDF Full Text: DOI
Anshelevich, Michael A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind. (English) Zbl 1347.33019 Integral Transforms Spec. Funct. 27, No. 4, 307-317 (2016). Reviewer: M. Abdessadek Saib (Tebessa) MSC: 33C45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Beatson, R. K.; zu Castell, W. One-step recurrences for stationary random fields on the sphere. (English) Zbl 1347.42009 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 043, 19 p. (2016). MSC: 42A82 60G60 60G10 42C10 33C45 62M30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Huang, Zhu; Boyd, John P. Bandwidth truncation for Chebyshev polynomial and ultraspherical/Chebyshev Galerkin discretizations of differential equations: restrictions and two improvements. (English) Zbl 1416.65478 J. Comput. Appl. Math. 302, 340-355 (2016). MSC: 65N35 65N12 × Cite Format Result Cite Review PDF Full Text: DOI
Driver, Kathy; Muldoon, Martin E. A connection between ultraspherical and pseudo-ultraspherical polynomials. (English) Zbl 1336.33030 J. Math. Anal. Appl. 439, No. 1, 323-329 (2016). MSC: 33C55 26C10 × Cite Format Result Cite Review PDF Full Text: DOI
Kahler, Stefan Characterizations of ultraspherical polynomials and their \(q\)-analogues. (English) Zbl 1332.33027 Proc. Am. Math. Soc. 144, No. 1, 87-101 (2016). Reviewer: Renato Alvarez-Nodarse (Sevilla) MSC: 33D45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Doha, E. H.; Abd-Elhameed, W. M. New connection formulae between ultraspherical polynomials and Chebyshev polynomials of third and fourth kinds. (English) Zbl 1333.42048 Adv. Stud. Contemp. Math., Kyungshang 25, No. 4, 511-524 (2015). MSC: 42C10 33C55 65L05 65L10 × Cite Format Result Cite Review PDF
Youssri, Y. H.; Elhameed, W. M. Abd-; Doha, E. H. Accurate spectral solutions of first- and second-order initial value problems by the ultraspherical wavelets-Gauss collocation method. (English) Zbl 1330.65125 Appl. Appl. Math. 10, No. 2, 835-851 (2015). MSC: 65L60 65T60 × Cite Format Result Cite Review PDF Full Text: Link
Aldenhoven, Noud Explicit matrix inverses for lower triangular matrices with entries involving continuous \(q\)-ultraspherical polynomials. (English) Zbl 1333.33024 J. Approx. Theory 199, 1-12 (2015). Reviewer: Roelof Koekoek (Delft) MSC: 33D45 33D15 42C05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kahler, Stefan Orthogonal polynomials and point and weak amenability of \(\ell ^1\)-algebras of polynomial hypergroups. (English) Zbl 1332.33015 Constr. Approx. 42, No. 1, 31-63 (2015). Reviewer: Jiří Hrivnák (Praha) MSC: 33C45 33C47 42C05 43A20 43A62 46H20 × Cite Format Result Cite Review PDF Full Text: DOI
Tikhanovtseva, K. S. The rate of the smallest value of the weighted measure of the nonnegativity set for polynomials with zero mean value on a closed interval. (English. Russian original) Zbl 1325.26038 Proc. Steklov Inst. Math. 288, Suppl. 1, S195-S201 (2015); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 20, No. 1, 264-270 (2014). Reviewer: Armin Rainer (Wien) MSC: 26C05 26C10 × Cite Format Result Cite Review PDF Full Text: DOI
Odake, Satoru; Sasaki, Ryu Reflectionless potentials for difference Schrödinger equations. (English) Zbl 1312.39010 J. Phys. A, Math. Theor. 48, No. 11, Article ID 115204, 21 p. (2015). MSC: 39A12 39A10 81Q05 33B15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nikolov, Geno; Pillwein, Veronika An extension of Turán’s inequality. (English) Zbl 1306.41004 Math. Inequal. Appl. 18, No. 1, 321-335 (2015). MSC: 41A17 68W30 × Cite Format Result Cite Review PDF Full Text: DOI
Erb, Wolfgang; Mathias, Sonja An alternative to Slepian functions on the unit sphere – a space-frequency analysis based on localized spherical polynomials. (English) Zbl 1307.42025 Appl. Comput. Harmon. Anal. 38, No. 2, 222-241 (2015). MSC: 42C10 42B05 45C05 47B36 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Markett, Clemens New representation and factorizations of the higher-order ultraspherical-type differential equations. (English) Zbl 1303.33023 J. Math. Anal. Appl. 421, No. 1, 244-259 (2015). Reviewer: Andrei A. Kapaev (St. Petersburg) MSC: 33E30 42C05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Abd-Elhameed, Waleed M.; Youssri, Youssri; Doha, Eid H. New solutions for singular Lane-Emden equations arising in astrophysics based on shifted ultraspherical operational matrices of derivatives. (English) Zbl 1412.65160 Comput. Methods Differ. Equ. 2, No. 3, 171-185 (2014). MSC: 65M70 65N35 35C10 42C10 × Cite Format Result Cite Review PDF Full Text: Link
El-Khateb, Mostafa A.; Almulla, Noha; Hasanien, Hussien S. Solving integro-differential equations systems by Galerkin method with orthogonal polynomials. (English) Zbl 1413.65481 J. Mod. Methods Numer. Math. 5, No. 2, 18-27 (2014). MSC: 65R20 65K10 41A10 45J05 × Cite Format Result Cite Review PDF Full Text: DOI
Nikolov, Geno Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa. (English) Zbl 1305.41017 J. Math. Anal. Appl. 418, No. 2, 852-860 (2014). MSC: 41A17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sharapudinov, I. I. Some special series in ultraspherical polynomials and their approximation properties. (English. Russian original) Zbl 1312.33033 Izv. Math. 78, No. 5, 1036-1059 (2014); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 78, No. 5, 201-224 (2014). Reviewer: Renato Alvarez-Nodarse (Sevilla) MSC: 33C45 41A58 42C10 × Cite Format Result Cite Review PDF Full Text: DOI
Driver, Kathy; Muldoon, Martin E. Zeros of pseudo-ultraspherical polynomials. (English) Zbl 1301.33011 Anal. Appl., Singap. 12, No. 5, 563-581 (2014). MSC: 33C45 33C47 × Cite Format Result Cite Review PDF Full Text: DOI
Aleksov, Dragomir I. An approach for derivation of Markov-type inequalities in \(L_2\) norms. (English) Zbl 1474.41017 God. Sofiĭ. Univ., Fak. Mat. Inform. 101, 215-235 (2013). MSC: 41A17 41A05 × Cite Format Result Cite Review PDF Full Text: Link
Nikolov, Geno P. On Turan’s inequality for ultraspherical polynomials. (English) Zbl 1474.41019 God. Sofiĭ. Univ., Fak. Mat. Inform. 101, 105-114 (2013). MSC: 41A17 33C45 × Cite Format Result Cite Review PDF Full Text: Link
Gupta, V. G.; Jangid, Nawal Kishor Some results on homogeneous generalized hypergeometric function and \(\overline H\)-function. (English) Zbl 1310.33008 Jñānābha 43, 97-106 (2013). MSC: 33C60 33C45 × Cite Format Result Cite Review PDF
Szabłowski, Paweł J. On the \(q\)-Hermite polynomials and their relationship with some other families of orthogonal polynomials. (English) Zbl 1290.33024 Demonstr. Math. 46, No. 4, 679-708 (2013). MSC: 33D45 05A30 42C05 × Cite Format Result Cite Review PDF Full Text: arXiv
Sharapudinov, I. I. Limit ultraspherical series and their approximation properties. (English. Russian original) Zbl 1279.42029 Math. Notes 94, No. 2, 281-293 (2013); translation from Mat. Zametki 94, No. 2, 295-309 (2013). MSC: 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Olver, Sheehan; Townsend, Alex A fast and well-conditioned spectral method. (English) Zbl 1273.65182 SIAM Rev. 55, No. 3, 462-489 (2013). MSC: 65N35 65L10 33C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Kokologiannaki, C. G.; Rizos, D. On the zeros of polynomials satisfying a three-term recurrence relation with complex coefficients. (English) Zbl 1312.33031 J. Inequal. Spec. Funct. 3, No. 3, 29-33 (2012). MSC: 33C45 × Cite Format Result Cite Review PDF
Verma, Alok; Ahmed, K. A new theorem on the Cesaro summability of an ultra spherical series. (English) Zbl 1296.40006 J. Indian Acad. Math. 34, No. 1, 291-299 (2012). MSC: 40G05 33C45 × Cite Format Result Cite Review PDF
Verma, Alok; Ahmed, K. A note on the convergence of series of ultraspherical polynomials. (English) Zbl 1292.33015 J. Indian Acad. Math. 34, No. 1, 185-188 (2012). MSC: 33C45 40A05 × Cite Format Result Cite Review PDF
Jung, Hee Sun; Sakai, Ryozi Asymptotic properties of derivatives of the Stieltjes polynomials. (English) Zbl 1252.41004 J. Appl. Math. 2012, Article ID 482935, 25 p. (2012). MSC: 41A05 41A10 × Cite Format Result Cite Review PDF Full Text: DOI
Berestovskiĭ, V. N. Zonal spherical functions on CROSS’s and special functions. (English. Russian original) Zbl 1253.53055 Sib. Math. J. 53, No. 4, 611-624 (2012); translation from Sib. Mat. Zh. 53, No. 4, 765-780 (2012). MSC: 53C35 53C20 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Xiang, Shuhuang On error bounds for orthogonal polynomial expansions and Gauss-type quadrature. (English) Zbl 1263.65027 SIAM J. Numer. Anal. 50, No. 3, 1240-1263 (2012). Reviewer: Ana-Maria Acu (Sibiu) MSC: 65D32 65D20 42C05 33C45 33F05 41A55 × Cite Format Result Cite Review PDF Full Text: DOI
Chapon, François Affine Dunkl processes of type \(\widetilde{\mathrm{A}}_{1}\). (English. French summary) Zbl 1255.60150 Ann. Inst. Henri Poincaré, Probab. Stat. 48, No. 3, 854-870 (2012). Reviewer: Michael Voit (Dortmund) MSC: 60J75 60J60 60B15 33C52 43A62 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Masjed-Jamei, Mohammad; Koepf, Wolfram Two classes of special functions using Fourier transforms of generalized ultraspherical and generalized Hermite polynomials. (English) Zbl 1246.33005 Proc. Am. Math. Soc. 140, No. 6, 2053-2063 (2012). Reviewer: Nele De Schepper (Gent) MSC: 33C45 42A38 × Cite Format Result Cite Review PDF Full Text: DOI
Cantero, María José; Iserles, Arieh On rapid computation of expansions in ultraspherical polynomials. (English) Zbl 1241.42023 SIAM J. Numer. Anal. 50, No. 1, 307-327 (2012). Reviewer: Manfred Tasche (Rostock) MSC: 42C10 33C45 65T50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Nadjafi, Jafar Saberi; Samadi, Omid Reza Navid; Tohidi, Emran Numerical solution of two-dimensional Volterra integral equations by spectral Galerkin method. (English) Zbl 1270.65079 J. Appl. Math. Bioinform. 1, No. 2, 159-174 (2011). MSC: 65R20 45D05 45G10 × Cite Format Result Cite Review PDF
Ismail, Mourad E. H.; Rahman, Mizan Connection relations and expansions. (English) Zbl 1235.05020 Pac. J. Math. 252, No. 2, 427-446 (2011). MSC: 05A30 05A19 33D15 33D70 × Cite Format Result Cite Review PDF Full Text: DOI Link
Betancor, Jorge J.; Fariña, Juan C.; Rodríguez-Mesa, Lourdes; Testoni, Ricardo Higher order Riesz transforms in the ultraspherical setting as principal value integral operators. (English) Zbl 1229.42025 Integral Equations Oper. Theory 70, No. 4, 511-539 (2011). Reviewer: H.-J. Glaeske (Jena) MSC: 42C05 42C15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Zhang, Ruiming; Chen, Li-Chen Matrix inversion using orthogonal polynomials. (English) Zbl 1216.33021 Arab J. Math. Sci. 17, No. 1, 11-30 (2011). MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Obermaier, Josef A modified Fejér and Jackson summability method with respect to orthogonal polynomials. (English) Zbl 1225.42018 J. Approx. Theory 163, No. 4, 554-567 (2011). Reviewer: H.-J. Glaeske (Jena) MSC: 42C05 33C45 40G99 × Cite Format Result Cite Review PDF Full Text: DOI
Ismail, Mourad E. H.; Obermaier, Josef Characterizations of continuous and discrete \(q\)-ultraspherical polynomials. (English) Zbl 1214.33010 Can. J. Math. 63, No. 1, 181-199 (2011). Reviewer: Nele De Schepper (Gent) MSC: 33D45 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Jordaan, K.; Toókos, F. Mixed recurrence relations and interlacing of the zeros of some \(q\)-orthogonal polynomials from different sequences. (English) Zbl 1224.26054 Acta Math. Hung. 128, No. 1-2, 150-164 (2010). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 26C10 33C45 × Cite Format Result Cite Review PDF Full Text: DOI Link
Masjed-Jamei, Mohammad; Koepf, Wolfram On incomplete symmetric orthogonal polynomials of Jacobi type. (English) Zbl 1206.33010 Integral Transforms Spec. Funct. 21, No. 9-10, 655-662 (2010). Reviewer: Thomas Stoll (Marseille) MSC: 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Moreno, Samuel G.; García-Caballero, Esther M. New orthogonality relations for the continuous and the discrete \(q\)-ultraspherical polynomials. (English) Zbl 1247.33032 J. Math. Anal. Appl. 369, No. 1, 386-399 (2010). Reviewer: Roelof Koekoek (Delft) MSC: 33D45 × Cite Format Result Cite Review PDF Full Text: DOI
Masjed-Jamei, Mohammad A basic class of symmetric orthogonal functions with six free parameters. (English) Zbl 1195.33068 J. Comput. Appl. Math. 234, No. 1, 283-296 (2010). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C47 05E05 34B24 42C05 × Cite Format Result Cite Review PDF Full Text: DOI
Betancor, Jorge J.; Fariña, Juan C.; Rodríguez-Mesa, Lourdes; Testoni, Ricardo; Torrea, José L. A choice of Sobolev spaces associated with ultraspherical expansions. (English) Zbl 1183.42026 Publ. Mat., Barc. 54, No. 1, 221-242 (2010). MSC: 42C05 42C15 × Cite Format Result Cite Review PDF Full Text: DOI Euclid Link
Demni, Nizar Ultraspherical type generating functions for orthogonal polynomials. (English) Zbl 1187.42023 Probab. Math. Stat. 29, No. 2, 281-296 (2009). MSC: 42C05 33C45 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Doha, E. H.; Abd-Elhameed, W. M.; Bhrawy, A. H. Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations. (English) Zbl 1205.65224 Appl. Math. Modelling 33, No. 4, 1982-1996 (2009). MSC: 65L60 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
El-Kady, M.; Ibrahim, M. A. Ultraspherical differentiation method for solving system of initial value differential algebraic equations. (English) Zbl 1183.41021 Comput. Methods Appl. Math. 9, No. 3, 226-237 (2009). MSC: 41A30 65L80 × Cite Format Result Cite Review PDF Full Text: DOI
Gonska, Heiner; Heilmann, Margareta; Raşa, Ioan Convergence of iterates of genuine and ultraspherical Durrmeyer operators to the limiting semigroup: \(C^{2}\)-estimates. (English) Zbl 1184.41005 J. Approx. Theory 160, No. 1-2, 243-255 (2009). Reviewer: Zoltán Finta (Cluj-Napoca) MSC: 41A10 41A17 41A25 41A36 × Cite Format Result Cite Review PDF Full Text: DOI
Waldron, Shayne Continuous and discrete tight frames of orthogonal polynomials for a radially symmetric weight. (English) Zbl 1180.33011 Constr. Approx. 30, No. 1, 33-52 (2009). Reviewer: Alicia Cachafeiro López (Vigo) MSC: 33C45 33D50 06B15 42C15 × Cite Format Result Cite Review PDF Full Text: DOI
Doha, E. H.; Abd-Elhameed, W. M. Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of \((2n + 1)\)th-order linear differential equations. (English) Zbl 1169.65326 Math. Comput. Simul. 79, No. 11, 3221-3242 (2009). MSC: 65L10 34B05 × Cite Format Result Cite Review PDF Full Text: DOI