贝特曼多项式
贝特曼多项式(Bateman polynomials)是一个正交多项式,定义如下[1]
其中 F为超几何函数,P是勒让得多项式
前几个贝特曼多项式为
- ;
- ;
- ;
- ;
- ;
- ;
参考文献
- ^ Bateman, H. (1933), "Some properties of a certain set of polynomials.", Tôhoku Mathematical Journal 37: 23–38
- Al-Salam, Nadhla A. A class of hypergeometric polynomials. Ann. Matem. Pura Applic. 1967, 75 (1): 95–120. doi:10.1007/BF02416800.
- Bateman, H., Some properties of a certain set of polynomials., Tôhoku Mathematical Journal, 1933, 37: 23–38, JFM 59.0364.02[失效链接]
- Carlitz, Leonard, Some polynomials of Touchard connected with the Bernoulli numbers, Canadian Journal of Mathematics, 1957, 9: 188–190 [2015-01-14], ISSN 0008-414X, MR 0085361, doi:10.4153/CJM-1957-021-9, (原始内容存档于2012-03-30)
- Koelink, H. T., On Jacobi and continuous Hahn polynomials, Proceedings of the American Mathematical Society, 1996, 124 (3): 887–898, ISSN 0002-9939, MR 1307541, doi:10.1090/S0002-9939-96-03190-5
- Pasternack, Simon, A generalization of the polynomial Fn(x), London, Edinburgh, Dublin Philosophical Magazine and Journal of Science, 1939, 28: 209–226, MR 0000698
- Touchard, Jacques, Nombres exponentiels et nombres de Bernoulli, Canadian Journal of Mathematics, 1956, 8: 305–320 [2015-01-14], ISSN 0008-414X, MR 0079021, doi:10.4153/cjm-1956-034-1, (原始内容存档于2012-03-30)