大q雅可比多项式
大q-雅可比多项式 （英語：Big q-Jacobi polynomials ）是一个以基本超几何函数 定义的正交多项式[ 1]
BIG Q JACOBI 2D Maple PLOT
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{\displaystyle \displaystyle P_{n}(x;a,b,c;q)={}_{3}\phi _{2}(q^{-n},abq^{n+1},x;aq,cq;q,q)}
大q-雅可比多项式满足下列正交关系
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{\displaystyle \sum _{x}(p_{n}(x)*p_{m}(x)|x|v_{x}=h_{n}*\delta _{m}n}
大q雅可比多项式→大q拉盖尔多项式 令大q雅可比多项式中的
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{\displaystyle b=0}
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{\displaystyle P_{n}(x;a,0,c;q)=P_{n}(x;a,c;q)}
BIG Q JACOBI ABS COMPLEX3D Maple PLOT2 BIG Q JACOBI IM COMPLEX3D Maple PLOT BIG Q JACOBI RE COMPLEX3D Maple PLOT
BIG Q JACOBI ABS COMPLEX DENSITY Maple PLOT BIG Q JACOBI IM COMPLEX DENSITY Maple PLOT BIG Q JACOBI RE COMPLEX DENSITY Maple PLOT
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 978-3-540-16059-5MR 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 978-0-521-83357-8MR 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 978-3-642-05013-8MR 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 , Olver, Frank W. J. ; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W. (编), NIST Handbook of Mathematical Functions , Cambridge University Press, 2010, ISBN 978-0521192255MR 2723248
^ Roelof p438
