33 citations · 182 across the 41 of their papers we have counts for
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A few identities and integrals involving Pochhammer symbols, Jacobi polynomials, and the generalized hypergeometric function
Paweł J. Szabłowski
We first present some identities involving the Pochhammer symbol (rising factorial). We also recall and present some new properties of the Jacobi polynomials. We use them to expand…
Moment sequences and difference equations
Paweł J. Szabłowski
We recall the definition and properties of a moment sequence and show that all real sequences whose Hankel matrices have finite rank (see definition in the sequel) satisfy a homoge…
On the families of polynomials forming a part of the Askey--Wilson scheme and their probabilistic applications
Paweł J. Szabłowski
We review the properties of six families of orthogonal polynomials that form the main bulk of the collection called the Askey--Wilson scheme of polynomials. We give connection coef…
Multivariate generating functions built of Chebyshev polynomials and some of its applications and generalizations
Paweł J. Szabłowski
We sum multivariate generating functions composed of products of Chebyshev polynomials of the first and the second kind. That is, we find closed forms of expressions of the type $\…
On probabilistic aspects of Chebyshev polynomials
Paweł J. Szabłowski
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea…
On affinity relating two positive measures and the connection coefficients between polynomials orthogonalized by these measures
Paweł J. Szabłowski
We consider two positive, normalized measures dA(x) and dB(x) related by the relationship dA(x)=(C/(x+D))dB(x) or by dA(x) = (C/(x^2+E))dB(x) and dB(x) is symmetric. We show that t…