1 citations · 1 across the 2 of their papers we have counts for
5 papers
Moment sequences and difference equations
PaweÅ J. SzabÅowski
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…
The conditional expectation of the product of the first Hermite polynomials in a multivariate normal distribution with respect to the -th variable. A fresh perspective on the Kibble-Slepian formula
PaweÅ J. SzabÅowski
We calculate the conditional expectation of given if random vector has multivariate normal distribution…
A few identities and integrals involving Pochhammer symbols, Jacobi polynomials, and the generalized hypergeometric function
PaweÅ J. SzabÅowski
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…
Applications of infinite lower triangular matrices and their group structure in combinatorics and the theory of orthogonal polynomials
PaweÅ J. SzabÅowski
Our focus is on the set of lower-triangular, infinite matrices that have natural operations like addition, multiplication by a number, and matrix multiplication. With respect to ad…
A few finite and infinite identities involving Pochhammer and - Pochhammer symbols obtained via analytical methods
PaweÅ J. SzabÅowski
We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these…