Linearization and Krein-like functionals of hypergeometric orthogonal polynomials

The Krein-like $r$-functionals of the hypergeometric orthogonal polynomials $\{p_n(x)\}$ with kernel of the form $x^s[\omega (x){]}^{\beta }{p}_{m_1}(x)\dots p_{m_r}(x)$, being $\omega (x)$ the weight function on the interval $\mathrm{\Delta }\in \mathbb{R}$, are determined by means of the Srivastava linearization method. The particular $2$-functionals, which are particularly relevant in quantum physics, are explicitly given in terms of the degrees and the characteristic parameters of the polynomials. They include the well-known power moments and the novel Krein-like moments. Moreover, various related types of exponential and logarithmic functionals are also investigated.