论文标题
某些特定正交多项式的结构关系
A structure relation for some specific orthogonal polynomials
论文作者
论文摘要
通过表征所有正交多项式序列$（p_n）_ {n \ geq 0} $，为哪个$$（ax+b）（\ triangle +2 \，\ mathrm {i}）p_n（x（s-1/2）） n = 0,1,2，\ dots，$$，其中$ \，\ mathrm {i} $是身份操作员，$ x $定义了$ q $ -quadratic lattice，$ \ triangle f（s）= f（s）= f（s+1）-f（s）-f（s）-f（S）$ $（b_n）_ {n \ geq0} $和$（c_n）_ {n \ geq0} $是复数的序列，我们为正交多发词的某些特定家族得出了一些新的结构关系。
By characterizing all orthogonal polynomials sequences $(P_n)_{n\geq 0}$ for which $$ (ax+b)(\triangle +2\,\mathrm{I})P_n(x(s-1/2))=(a_n x+b_n)P_n(x)+c_n P_{n-1}(x),\quad n=0,1,2,\dots, $$ where $\,\mathrm{I}$ is the identity operator, $x$ defines a $q$-quadratic lattice, $\triangle f(s)=f(s+1)-f(s)$, and $(a_n)_{n\geq0}$, $(b_n)_{n\geq0}$ and $(c_n)_{n\geq0}$ are sequences of complex numbers, we derive some new structure relations for some specific families of orthogonal polynomials.
