离散q-埃尔米特I多项式维基百科,自由的 encyclopedia 离散q-埃尔米特多项式是以超几何函数定义的正交多项式[1] h n ( x ; q ) = q ( n 2 ) 2 ϕ 1 ( q − n , x − 1 ; 0 ; q , − q x ) = x n 2 ϕ 0 ( q − n , q − n + 1 ; ; q 2 , q 2 n − 1 / x 2 ) = U n ( − 1 ) ( x ; q ) {\displaystyle \displaystyle h_{n}(x;q)=q^{\binom {n}{2}}{}_{2}\phi _{1}(q^{-n},x^{-1};0;q,-qx)=x^{n}{}_{2}\phi _{0}(q^{-n},q^{-n+1};;q^{2},q^{2n-1}/x^{2})=U_{n}^{(-1)}(x;q)}
离散q-埃尔米特多项式是以超几何函数定义的正交多项式[1] h n ( x ; q ) = q ( n 2 ) 2 ϕ 1 ( q − n , x − 1 ; 0 ; q , − q x ) = x n 2 ϕ 0 ( q − n , q − n + 1 ; ; q 2 , q 2 n − 1 / x 2 ) = U n ( − 1 ) ( x ; q ) {\displaystyle \displaystyle h_{n}(x;q)=q^{\binom {n}{2}}{}_{2}\phi _{1}(q^{-n},x^{-1};0;q,-qx)=x^{n}{}_{2}\phi _{0}(q^{-n},q^{-n+1};;q^{2},q^{2n-1}/x^{2})=U_{n}^{(-1)}(x;q)}