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Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the exponential generating function has a nice form. In the opposite direction, we show that the generalized Dumont-Foata polynomials with six parameters are the moments of rescaled continuous dual Hahn polynomials.
We present a formula that expresses the Hankel determinants of a linear combination of length $d+1$ of moments of orthogonal polynomials in terms of a $dtimes d$ determinant of the orthogonal polynomials. This formula exists somehow hidden in the fol
Let $p_n(x)$, $n=0,1,dots$, be the orthogonal polynomials with respect to a given density $dmu(x)$. Furthermore, let $d u(x)$ be a density which arises from $dmu(x)$ by multiplication by a rational function in $x$. We prove a formula that expresses t
We introduce a new family of orthogonal polynomials on the disk that has emerged in the context of wave propagation in layered media. Unlike known examples, the polynomials are orthogonal with respect to a measure all of whose even moments are infinite.
We derive the P-finite recurrences for classes of sequences with ordinary generating function containing roots of polynomials. The focus is on establishing the D-finite differential equations such that the familiar steps of reducing their power series expansions apply.
Let $G$ be a topological commutative semigroup with unit. We prove that a continuous function $fcolon Gto cc$ is a generalized exponential polynomial if and only if there is an $nge 2$ such that $f(x_1 +ldots +x_n )$ is decomposable; that is, if $f(x