Chebyshev polynomials (English Wikipedia)

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

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12doi.org

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4archive.org

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3ams.org

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2wikipedia.org

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1arxiv.org

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1ubc.ca

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ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

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 (Global: 6^th place; English: 6^th place)

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 (Global: 69^th place; English: 59^th place)

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 (Global: 124^th place; English: 544^th place)

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 (Global: 3^rd place; English: 3^rd place)

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 (Global: 887^th place; English: 714^th place)

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 (Global: 2^nd place; English: 2^nd place)

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 (Global: 70^th place; English: 63^rd place)

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 (Global: low place; English: low place)

fq.math.ca

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

nasa.gov (Global: 75^th place; English: 83^rd place)

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 (Global: 3,707^th place; English: 2,409^th place)

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 (Global: low place; English: low place)

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

semanticscholar.org (Global: 11^th place; English: 8^th place)

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 (Global: 1,997^th place; English: 1,295^th place)

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 (Global: 3,695^th place; English: 3,560^th place)

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 (Global: 459^th place; English: 360^th place)

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 (Global: 1^st place; English: 1^st place)

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 (Global: low place; English: low place)

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 (Global: 5^th place; English: 5^th place)

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.

Chebyshev polynomials (English Wikipedia)

ams.org (Global: 451st place; English: 277th place)

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ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 69th place; English: 59th place)

bnf.fr (Global: 124th place; English: 544th place)

gallica.bnf.fr

books.google.com (Global: 3rd place; English: 3rd place)

caltech.edu (Global: 887th place; English: 714th place)

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doi.org (Global: 2nd place; English: 2nd place)

loc.gov (Global: 70th place; English: 63rd place)

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math.ca (Global: low place; English: low place)

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nasa.gov (Global: 75th place; English: 83rd place)

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projecteuclid.org (Global: 3,707th place; English: 2,409th place)

scottsarra.org (Global: low place; English: low place)

semanticscholar.org (Global: 11th place; English: 8th place)

api.semanticscholar.org

ubc.ca (Global: 1,997th place; English: 1,295th place)

personal.math.ubc.ca

ugent.be (Global: 3,695th place; English: 3,560th place)

cage.ugent.be

umich.edu (Global: 459th place; English: 360th place)

www-personal.umich.edu

web.archive.org (Global: 1st place; English: 1st place)

wikipedia.org (Global: low place; English: low place)

de.wikipedia.org

worldcat.org (Global: 5th place; English: 5th place)

search.worldcat.org

ams.org (Global: 451^st place; English: 277^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 69^th place; English: 59^th place)

bnf.fr (Global: 124^th place; English: 544^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

caltech.edu (Global: 887^th place; English: 714^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

loc.gov (Global: 70^th place; English: 63^rd place)

nasa.gov (Global: 75^th place; English: 83^rd place)

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

semanticscholar.org (Global: 11^th place; English: 8^th place)

ubc.ca (Global: 1,997^th place; English: 1,295^th place)

ugent.be (Global: 3,695^th place; English: 3,560^th place)

umich.edu (Global: 459^th place; English: 360^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

worldcat.org (Global: 5^th place; English: 5^th place)