羅傑斯多項式
羅傑斯多項式又稱連續q超球面多項式是一個以超幾何函數定義的超幾何正交多項式[1]
其中 x = cos(θ).即
極限關係
圖集
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參考文獻
- Askey, Richard; Ismail, Mourad E. H., A generalization of ultraspherical polynomials, Erdős, Paul (編), Studies in pure mathematics. To the memory of Paul Turán., Basel, Boston, Berlin: Birkhäuser: 55–78, 1983 [2015-01-30], ISBN 978-3-7643-1288-6, MR 0820210, (原始內容存檔於2014-01-05)
- Gasper, George; Rahman, Mizan, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
- Macdonald, I. G., Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts in Mathematics 157, Cambridge University Press, 2003, ISBN 978-0-521-82472-9, MR 1976581, doi:10.1017/CBO9780511542824
- Rogers, L. J., On the expansion of some infinite products, Proc. London Math. Soc., 1892, 24 (1): 337–352, JFM 25.0432.01, doi:10.1112/plms/s1-24.1.337
- Rogers, L. J., Second Memoir on the Expansion of certain Infinite Products, Proc. London Math. Soc., 1893, 25 (1): 318–343, doi:10.1112/plms/s1-25.1.318
- Rogers, L. J., Third Memoir on the Expansion of certain Infinite Products, Proc. London Math. Soc., 1894, 26 (1): 15–32, doi:10.1112/plms/s1-26.1.15
參考文獻
- ^ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues,p469,Springer 2010
- Askey, Richard; Ismail, Mourad E. H., A generalization of ultraspherical polynomials, Erdős, Paul (編), Studies in pure mathematics. To the memory of Paul Turán., Basel, Boston, Berlin: Birkhäuser: 55–78, 1983 [2015-01-30], ISBN 978-3-7643-1288-6, MR 0820210, (原始內容存檔於2014-01-05)
- Gasper, George; Rahman, Mizan, Basic hypergeometric series, Encyclopedia of Mathematics and its Applications 96 2nd, Cambridge University Press, 2004, ISBN 978-0-521-83357-8, MR 2128719, doi:10.2277/0521833574
- Macdonald, I. G., Affine Hecke algebras and orthogonal polynomials, Cambridge Tracts in Mathematics 157, Cambridge University Press, 2003, ISBN 978-0-521-82472-9, MR 1976581, doi:10.1017/CBO9780511542824
- Rogers, L. J., On the expansion of some infinite products, Proc. London Math. Soc., 1892, 24 (1): 337–352, JFM 25.0432.01, doi:10.1112/plms/s1-24.1.337
- Rogers, L. J., Second Memoir on the Expansion of certain Infinite Products, Proc. London Math. Soc., 1893, 25 (1): 318–343, doi:10.1112/plms/s1-25.1.318
- Rogers, L. J., Third Memoir on the Expansion of certain Infinite Products, Proc. London Math. Soc., 1894, 26 (1): 15–32, doi:10.1112/plms/s1-26.1.15