Chebyshev polynomials (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Chebyshev polynomials" in English language version.

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Beckenbach, E. F.; Seidel, W.; Szász, Otto (1951), "Recurrent determinants of Legendre and of ultraspherical polynomials", Duke Math. J., 18: 1–10, doi:10.1215/S0012-7094-51-01801-7, MR 0040487
Hochstrasser 1972, p. 778. Hochstrasser, Urs W. (1972) [1964]. "Orthogonal Polynomials". In Abramowitz, Milton; Stegun, Irene (eds.). Handbook of Mathematical Functions (10th printing, with corrections; first ed.). Washington D.C.: National Bureau of Standards. Ch. 22, pp. 771–792. LCCN 64-60036. MR 0167642. Reprint: 1983. New York: Dover. ISBN 978-0-486-61272-0.

ams.org

Ritt, J. F. (1922). "Prime and Composite Polynomials". Trans. Amer. Math. Soc. 23: 51–66. doi:10.1090/S0002-9947-1922-1501189-9.

archive.org

Chebyshev first presented his eponymous polynomials in a paper read before the St. Petersburg Academy in 1853:
Chebyshev, P. L. (1854). "Théorie des mécanismes connus sous le nom de parallélogrammes". Mémoires des Savants étrangers présentés à l'Académie de Saint-Pétersbourg (in French). 7: 539–586. Also published separately as Chebyshev, P. L. (1853). Théorie des mécanismes connus sous le nom de parallélogrammes. St. Petersburg: Imprimerie de l'Académie Impériale des Sciences. doi:10.3931/E-RARA-120037.
Bateman & Bateman Manuscript Project 1953, p. 184, eqs. 3–4. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.
Bateman & Bateman Manuscript Project 1953, p. 187, eqs. 47–48. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.
Saal, Rudolf (January 1979). Handbook of Filter Design (in English and German) (1st ed.). Munich, Germany: Allgemeine Elektricitais-Gesellschaft. pp. 25, 26, 56–61, 116, 117. ISBN 3-87087-070-2.

arxiv.org

Mathar, Richard J. (2006). "Chebyshev series expansion of inverse polynomials". Journal of Computational and Applied Mathematics. 196 (2): 596–607. arXiv:math/0403344. doi:10.1016/j.cam.2005.10.013.

bnf.fr

gallica.bnf.fr

Viète, François (1646). Francisci Vietae Opera mathematica : in unum volumen congesta ac recognita / opera atque studio Francisci a Schooten (PDF). Bibliothèque nationale de France.

books.google.com

Mason & Handscomb 2002. Mason, J. C.; Handscomb, D.C. (2002). Chebyshev Polynomials. Chapman and Hall/CRC. doi:10.1201/9781420036114. ISBN 978-1-4200-3611-4.

caltech.edu

authors.library.caltech.edu

Bateman & Bateman Manuscript Project 1953, p. 184, eqs. 3–4. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.
Bateman & Bateman Manuscript Project 1953, p. 187, eqs. 47–48. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.

doi.org

Lanczos, C. (1952). "Solution of systems of linear equations by minimized iterations". Journal of Research of the National Bureau of Standards. 49 (1): 33. doi:10.6028/jres.049.006.
Chebyshev first presented his eponymous polynomials in a paper read before the St. Petersburg Academy in 1853:
Chebyshev, P. L. (1854). "Théorie des mécanismes connus sous le nom de parallélogrammes". Mémoires des Savants étrangers présentés à l'Académie de Saint-Pétersbourg (in French). 7: 539–586. Also published separately as Chebyshev, P. L. (1853). Théorie des mécanismes connus sous le nom de parallélogrammes. St. Petersburg: Imprimerie de l'Académie Impériale des Sciences. doi:10.3931/E-RARA-120037.
Schaeffer, A. C. (1941). "Inequalities of A. Markoff and S. Bernstein for polynomials and related functions". Bulletin of the American Mathematical Society. 47 (8): 565–579. doi:10.1090/S0002-9904-1941-07510-5. ISSN 0002-9904.
Ritt, J. F. (1922). "Prime and Composite Polynomials". Trans. Amer. Math. Soc. 23: 51–66. doi:10.1090/S0002-9947-1922-1501189-9.
Beckenbach, E. F.; Seidel, W.; Szász, Otto (1951), "Recurrent determinants of Legendre and of ultraspherical polynomials", Duke Math. J., 18: 1–10, doi:10.1215/S0012-7094-51-01801-7, MR 0040487
Mason & Handscomb 2002. Mason, J. C.; Handscomb, D.C. (2002). Chebyshev Polynomials. Chapman and Hall/CRC. doi:10.1201/9781420036114. ISBN 978-1-4200-3611-4.
Cody, W. J. (1970). "A survey of practical rational and polynomial approximation of functions". SIAM Review. 12 (3): 400–423. doi:10.1137/1012082.
Mathar, Richard J. (2006). "Chebyshev series expansion of inverse polynomials". Journal of Computational and Applied Mathematics. 196 (2): 596–607. arXiv:math/0403344. doi:10.1016/j.cam.2005.10.013.
Gürtaş, Y. Z. (2017). "Chebyshev Polynomials and the minimal polynomial of $\cos(2\pi /n)$ ". American Mathematical Monthly. 124 (1): 74–78. doi:10.4169/amer.math.monthly.124.1.74. S2CID 125797961.
Wolfram, D. A. (2022). "Factoring Chebyshev polynomials of the first and second kinds with minimal polynomials of $\cos(2\pi /d)$ ". American Mathematical Monthly. 129 (2): 172–176. doi:10.1080/00029890.2022.2005391. S2CID 245808448.
Rayes, M. O.; Trevisan, V.; Wang, P. S. (2005), "Factorization properties of chebyshev polynomials", Computers & Mathematics with Applications, 50 (8–9): 1231–1240, doi:10.1016/j.camwa.2005.07.003
Mason, J. C.; Elliott, G. H. (1993), "Near-minimax complex approximation by four kinds of Chebyshev polynomial expansion", J. Comput. Appl. Math., 46 (1–2): 291–300, doi:10.1016/0377-0427(93)90303-S

loc.gov

lccn.loc.gov

Bateman & Bateman Manuscript Project 1953, p. 184, eqs. 3–4. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.
Bateman & Bateman Manuscript Project 1953, p. 187, eqs. 47–48. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.
Hochstrasser 1972, p. 778. Hochstrasser, Urs W. (1972) [1964]. "Orthogonal Polynomials". In Abramowitz, Milton; Stegun, Irene (eds.). Handbook of Mathematical Functions (10th printing, with corrections; first ed.). Washington D.C.: National Bureau of Standards. Ch. 22, pp. 771–792. LCCN 64-60036. MR 0167642. Reprint: 1983. New York: Dover. ISBN 978-0-486-61272-0.

math.ca

fq.math.ca

Horadam, A. F. (2002), "Vieta polynomials" (PDF), Fibonacci Quarterly, 40 (3): 223–232

nasa.gov

ntrs.nasa.gov

Desmarais, Robert N.; Bland, Samuel R. (1995), "Tables of properties of airfoil polynomials", NASA Reference Publication 1343, National Aeronautics and Space Administration

projecteuclid.org

Schaeffer, A. C. (1941). "Inequalities of A. Markoff and S. Bernstein for polynomials and related functions". Bulletin of the American Mathematical Society. 47 (8): 565–579. doi:10.1090/S0002-9904-1941-07510-5. ISSN 0002-9904.

scottsarra.org

"Chebyshev Interpolation: An Interactive Tour". Archived from the original on 18 March 2017. Retrieved 2 June 2016.

semanticscholar.org

api.semanticscholar.org

Gürtaş, Y. Z. (2017). "Chebyshev Polynomials and the minimal polynomial of $\cos(2\pi /n)$ ". American Mathematical Monthly. 124 (1): 74–78. doi:10.4169/amer.math.monthly.124.1.74. S2CID 125797961.
Wolfram, D. A. (2022). "Factoring Chebyshev polynomials of the first and second kinds with minimal polynomials of $\cos(2\pi /d)$ ". American Mathematical Monthly. 129 (2): 172–176. doi:10.1080/00029890.2022.2005391. S2CID 245808448.

ubc.ca

personal.math.ubc.ca

Hochstrasser 1972, p. 778. Hochstrasser, Urs W. (1972) [1964]. "Orthogonal Polynomials". In Abramowitz, Milton; Stegun, Irene (eds.). Handbook of Mathematical Functions (10th printing, with corrections; first ed.). Washington D.C.: National Bureau of Standards. Ch. 22, pp. 771–792. LCCN 64-60036. MR 0167642. Reprint: 1983. New York: Dover. ISBN 978-0-486-61272-0.

ugent.be

cage.ugent.be

Demeyer, Jeroen (2007). Diophantine Sets over Polynomial Rings and Hilbert's Tenth Problem for Function Fields (PDF) (Ph.D. thesis). p. 70. Archived from the original (PDF) on 2 July 2007.

umich.edu

www-personal.umich.edu

Boyd, John P. (2001). Chebyshev and Fourier Spectral Methods (PDF) (second ed.). Dover. ISBN 0-486-41183-4. Archived from the original (PDF) on 31 March 2010. Retrieved 19 March 2009.

web.archive.org

Demeyer, Jeroen (2007). Diophantine Sets over Polynomial Rings and Hilbert's Tenth Problem for Function Fields (PDF) (Ph.D. thesis). p. 70. Archived from the original (PDF) on 2 July 2007.
Boyd, John P. (2001). Chebyshev and Fourier Spectral Methods (PDF) (second ed.). Dover. ISBN 0-486-41183-4. Archived from the original (PDF) on 31 March 2010. Retrieved 19 March 2009.
"Chebyshev Interpolation: An Interactive Tour". Archived from the original on 18 March 2017. Retrieved 2 June 2016.

wikipedia.org

de.wikipedia.org

Bateman & Bateman Manuscript Project 1953, p. 184, eqs. 3–4. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.
Bateman & Bateman Manuscript Project 1953, p. 187, eqs. 47–48. Bateman, Harry; Bateman Manuscript Project (1953). "Tchebichef polynomials". In Erdélyi, Arthur (ed.). Higher Transcendental Functions. Vol. 2. Research associates: W. Magnus, F. Oberhettinger [de], F. Tricomi (1st ed.). New York: McGraw-Hill. § 10.11, pp. 183–187. LCCN 53-5555. Caltech eprint 43491. Reprint: 1981. Melbourne, FL: Krieger. ISBN 0-89874-069-X.

worldcat.org

search.worldcat.org

Schaeffer, A. C. (1941). "Inequalities of A. Markoff and S. Bernstein for polynomials and related functions". Bulletin of the American Mathematical Society. 47 (8): 565–579. doi:10.1090/S0002-9904-1941-07510-5. ISSN 0002-9904.