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 $x^{s}[ω(x)]^βp_{m_{1}}(x)\ldots p_{m_{r}}(x)$, being $ω(x)$ the weight function on the interval $Δ\in\mathbb{R}$, 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.