连续q雅可比多项式维基百科,自由的 encyclopedia 连续q雅可比多项式定义如下 P n ( α ; β ) ( x | q ) = {\displaystyle P_{n}^{(\alpha ;\beta )}(x|q)=} ( q α + 1 ; q ) n ( q ; q ; ) n {\displaystyle {\frac {(q^{\alpha +1};q)_{n}}{(q;q;)_{n}}}} 4 Φ 3 {\displaystyle _{4}\Phi _{3}} ( q − n , q n + α + β + 1 ; q α / 2 + 1 / 4 e i θ ; q α / 2 + 1 / 4 e − i θ ) {\displaystyle (q^{-n},q^{n+\alpha +\beta +1};q^{\alpha /2+1/4}e^{i\theta };q^{\alpha /2+1/4}e^{-i\theta })}
连续q雅可比多项式定义如下 P n ( α ; β ) ( x | q ) = {\displaystyle P_{n}^{(\alpha ;\beta )}(x|q)=} ( q α + 1 ; q ) n ( q ; q ; ) n {\displaystyle {\frac {(q^{\alpha +1};q)_{n}}{(q;q;)_{n}}}} 4 Φ 3 {\displaystyle _{4}\Phi _{3}} ( q − n , q n + α + β + 1 ; q α / 2 + 1 / 4 e i θ ; q α / 2 + 1 / 4 e − i θ ) {\displaystyle (q^{-n},q^{n+\alpha +\beta +1};q^{\alpha /2+1/4}e^{i\theta };q^{\alpha /2+1/4}e^{-i\theta })}