# Linearization and Krein-like functionals of hypergeometric orthogonal polynomials

## TL;DR

This paper derives explicit formulas for Krein-like functionals of hypergeometric orthogonal polynomials using linearization, with applications to quantum physics and new insights into moments and related functionals.

## Contribution

It introduces a method to explicitly compute Krein-like functionals of hypergeometric orthogonal polynomials, including novel moments and exponential/logarithmic functionals.

## Key findings

- Explicit formulas for Krein-like functionals are obtained.
- Power and Krein-like moments are characterized in terms of polynomial parameters.
- Various exponential and logarithmic functionals are analyzed.

## Abstract

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 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.