大q雅可比多项式：修订间差异
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:<math>\displaystyle P_n(x;a,b,c;q)={}_3\phi_2(q^{-n},abq^{n+1},x;aq,cq;q,q) </math> |
:<math>\displaystyle P_n(x;a,b,c;q)={}_3\phi_2(q^{-n},abq^{n+1},x;aq,cq;q,q) </math> |
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==参考文献== |
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*{{Citation | last1=Andrews | first1=George E. |authorlink1=George Andrews (mathematician)| last2=Askey | first2=Richard |authorlink2=Richard Askey | editor1-last=Brezinski | editor1-first=C. | editor2-last=Draux | editor2-first=A. | editor3-last=Magnus | editor3-first=Alphonse P. | editor4-last=Maroni | editor4-first=Pascal | editor5-last=Ronveaux | editor5-first=A. | title=Polynômes orthogonaux et applications. Proceedings of the Laguerre symposium held at Bar-le-Duc, October 15–18, 1984. | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Lecture Notes in Math. | isbn=978-3-540-16059-5 | mr=838970 | year=1985 | volume=1171 | chapter=Classical orthogonal polynomials | doi=10.1007/BFb0076530 | pages=36–62}} |
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*{{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=[[Cambridge University Press]] | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | doi=10.2277/0521833574 | mr=2128719 | year=2004 | volume=96}} |
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*{{Citation | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010}} |
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*{{dlmf|id=18|title=|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}} |
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2015年1月26日 (一) 12:40的版本
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大q-雅可比多项式是一个以基本超几何函数定义的正交多项式：
参考文献
- Andrews, George E.; Askey, Richard, Classical orthogonal polynomials, Brezinski, C.; Draux, A.; Magnus, Alphonse P.; Maroni, Pascal; Ronveaux, A. (编), Polynômes orthogonaux et applications. Proceedings of the Laguerre symposium held at Bar-le-Duc, October 15–18, 1984., Lecture Notes in Math. 1171, Berlin, New York: Springer-Verlag: 36–62, 1985, ISBN 978-3-540-16059-5, MR 0838970, doi:10.1007/BFb0076530
- 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