On the eigenstructure of the q-Stancu operator

The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, Ln,s,q, introduced by L. Yun and R. Wang. In this work, an explicit representation for moments of all orders has been derived. Further, it has been proved that Ln,s,q possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived. In addition, for special choices of parameters, several eigenfunctions are depicted.