小q拉盖尔多项式
极限关系
- 大q拉盖尔多项式→小q拉盖尔多项式
在大q拉盖尔多项式中,令 ,并令 即得小q拉盖尔多项式
仿射Q克拉夫楚克多项式→ 小q拉盖尔多项式:
令小q拉盖尔多项式 ,然后令q→1 即得拉盖尔多项式
- 验证 9阶小q拉盖尔多项式→拉盖尔多项式
作上述代换,
令a=3,得
另一方面
=
二者显然相等 QED
图集
参考文献
- Chihara, Theodore Seio, An introduction to orthogonal polynomials, Mathematics and its Applications 13, New York: Gordon and Breach Science Publishers, 1978 [2015-02-06], ISBN 978-0-677-04150-6, MR 0481884, Reprinted by Dover 2011,
- 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
- Koekoek, Roelof; Lesky, Peter A.; Swarttouw, René F., Hypergeometric orthogonal polynomials and their q-analogues, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, 2010, ISBN 978-3-642-05013-8, MR 2656096, doi:10.1007/978-3-642-05014-5
- Koornwinder, Tom H.; Wong, Roderick S. C.; Koekoek, Roelof; Swarttouw, René F., http://dlmf.nist.gov/18
|contribution-url=
缺少标题 (帮助), Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248 - Van Assche, Walter; Koornwinder, Tom H., Asymptotic behaviour for Wall polynomials and the addition formula for little q-Legendre polynomials, SIAM Journal on Mathematical Analysis, 1991, 22 (1): 302–311, ISSN 0036-1410, MR 1080161, doi:10.1137/0522019
- Wall, H. S., A continued fraction related to some partition formulas of Euler, The American Mathematical Monthly, 1941, 48: 102–108, ISSN 0002-9890, JSTOR 2303599, MR 0003641