直交多項式
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2020/05/05 08:00 UTC 版)
数学における直交多項式列（ちょっこうたこうしきれつ、英: orthogonal polynomial sequence）または直交多項式系 (system of orthogonal polynomials) は、多項式の成す族（多項式列）であって、それに属するどの二つの多項式も適当な内積に関して直交するものをいう[1][2][3][4]。
- ^ a b c d e f g h i j k l m n o p q r s 時弘哲治、工学における特殊関数、共立出版。
- ^ a b c d e f g h i j k 青本和彦: 直交多項式入門, 数学書房, 2013 年.
- ^ a b c d e f g h i Hazewinkel, Michiel, ed. (2001), “Orthogonal polynomials”, Encyclopaedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- ^ a b c d e f g h Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 22". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 773. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253。
- ^ a b c d e f 山本哲朗『数値解析入門』サイエンス社〈サイエンスライブラリ 現代数学への入門 14〉、2003年6月、増訂版。ISBN 4-7819-1038-6。
- ^ a b c d e Koekoek, R., & Swarttouw, R. F. (1996). The Askey-scheme of hypergeometric orthogonal polynomials and its -analogue. arXiv preprint math/9602214.
- ^ a b c d e f Andrews, G. E., Askey, R., & Roy, R. (1999). Special functions. en:Cambridge university press.
- ^ a b c d Hahn, Wolfgang (1949), "Über Orthogonalpolynome, die q-Differenzengleichungen genügen", Mathematische Nachrichten, 2: 4–34, doi:10.1002/mana.19490020103, ISSN 0025-584X, MR 0030647
- ^ a b c Koekoek, R., Lesky, P. A., & Swarttouw, R. F. (2010). Hypergeometric orthogonal polynomials and their -analogues. en:Springer Science & Business Media.
- ^ a b c Ismail, Mourad E. H. (2005). Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge: Cambridge Univ. Press. ISBN 0-521-78201-5
- ^ a b c Askey, Richard; Wilson, James (1985), "Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials", Memoirs of the en:American Mathematical Society, 54 (319): iv+55, doi:10.1090/memo/0319, ISBN 978-0-8218-2321-7, ISSN 0065-9266, MR 0783216
- ^ Favard theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Favard_theorem&oldid=43634
- ^ J. Favard, "Sur les polynomes de Tchebicheff" C.R. Acad. Sci. Paris , 200 (1935) pp. 2052-2053
- ^ 森正武、数値解析第2版、共立出版。
- ^ Notaris, S. E. (2016). Gauss–Kronrod quadrature formulae–a survey of fifty years of research. Electron. Trans. Numer. Anal, 45, 371-404.
- ^ a b Ismail, M. E., & Zhang, R. (2017). A review of multivariate orthogonal polynomials. Journal of the Egyptian Mathematical Society, 25(2), 91-110.
- ^ Dunkl, C. F., & Xu, Y. (2014). Orthogonal polynomials of several variables. en:Cambridge University Press.
- ^ Langer, R. (2008). Symmetric functions and Macdonald polynomials.
- ^ a b c Kuznetsov, V. B. (2006). Workshop on Jack, Hall-Littlewood, and Macdonald Polynomials, September 23-26, 2003, ICMS, Edinburgh, United Kingdom. en:American Mathematical Society.
- ^ Szegő, Gábor (1939). Orthogonal Polynomials. Colloquium Publications. XXIII. en:American Mathematical Society. ISBN 978-0-8218-1023-1. MR0372517
- ^ Chihara, Theodore Seio (1978). An Introduction to Orthogonal Polynomials. Gordon and Breach, New York. ISBN 0-677-04150-0
- ^ Chihara, Theodore Seio (2001). 45 years of orthogonal polynomials: a view from the wings. “Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications (Patras, 1999)”. en:Journal of Computational and Applied Mathematics 133 (1): 13–21. doi:10.1016/S0377-0427(00)00632-4. ISSN 0377-0427. MR1858267
- ^ Orthogonal polynomials: computation and approximation, en:Oxford University Press, Oxford, 2004.
- ^ Orthogonal polynomials in MATLAB: exercises and solutions, SIAM, Philadelphia, 2016.
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