New analytic properties of nonstandard Sobolev-type Charlier orthogonal polynomials

In this contribution, we consider the sequence {Qnλ}n≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{Q_{n}^{\lambda }\}_{n\geq 0}$\end{document} of monic polynomials orthogonal with respect to the following inner product involving differences 〈p,q〉λ=∫0∞pxqxdψ(a)(x)+λΔp(c)Δq(c),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle p,q\rangle_{\lambda }={\int}_{0}^{\infty }p\left( x\right) q\left( x\right) d\psi^{(a)}(x)+\lambda {\Delta} p(c){\Delta} q(c), $$\end{document}