Generalized little $q$-Jacobi polynomials as eigensolutions of higher-order $q$-difference operators
Generalized little $q$-Jacobi polynomials as eigensolutions of higher-order $q$-difference operators
We consider the polynomials $p_n(x;a,b;M)$ obtained from the little $q$-Jacobi polynomials $p_n(x;a, b)$ by inserting a discrete mass $M$ at $x=0$ in the orthogonality measure. We show that for $a=q^j, \; j=0,1,2,\dots$, the polynomials $p_n(x;a,b;M)$ are eigensolutions of a linear $q$-difference operator of order $2j+4$ with polynomial coefficients. This provides …