斯蒂爾吉斯-維格特多項式

Stieltjes-Wigert polynomails

斯蒂爾吉斯-維格特多項式是一個以基本超幾何函數定義的正交多項式

$\displaystyle S_{n}(x;q)={\frac {1}{(q;q)_{n})}}{}_{1}\phi _{1}(q^{-n},0;q,-q^{n+1}x)$

極限關係

Q拉蓋爾多項式→斯蒂爾吉斯-維格特多項式

$\lim _{\alpha \to \infty }(xq^{-\alpha };q)=S_{n}(x;q)$

Q貝塞爾多項式→斯蒂爾吉斯-維格特多項式

Q查理耶多項式→斯蒂爾吉斯-維格特多項式

斯蒂爾吉斯-維格特多項式→埃爾米特多項式

參考文獻

• 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., Ch. 18, Orthogonal polynomials, Olver, Frank W. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (編), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010, ISBN 978-0521192255, MR2723248 
• Szegő, Gábor, Orthogonal Polynomials, Colloquium Publications 23, American Mathematical Society, Fourth Edition, 1975, ISBN 978-0-8218-1023-1, MR 0372517 
• Stieltjes, T. -J., Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 1894, VIII: 1–122 [2015-02-07], JFM 25.0326.01, MR 1344720, （原始內容存檔於2015-02-07） （法語） 
• Wigert, S., Sur les polynomes orthogonaux et l'approximation des fonctions continues, Arkiv för matematik, astronomi och fysik, 1923, 17: 1–1, JFM 49.0296.01 （法語）