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The Krein-like $r$-functionals of the hypergeometric orthogonal polynomials$\{p_{n}(x) \}$ with kernel of the form$x^{s}[\omega(x)]^{\beta}p_{m_{1}}(x)\ldots p_{m_{r}}(x)$, being $\omega(x)$the weight function on the interval $\Delta\in\mathbb{R}$, are determined bymeans of the Srivastava linearization method. The particular $2$-functionals,which are particularly relevant in quantum physics, are explicitly given interms of the degrees and the characteristic parameters of the polynomials. Theyinclude the well-known power moments and the novel Krein-like moments.Moreover, various related types of exponential and logarithmic functionals arealso investigated.

Linearization and Krein-like functionals of hypergeometric orthogonal polynomials