33 citations · 182 across the 41 of their papers we have counts for
44 papers
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
Paweł J. Szabłowski
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
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…
A few finite and infinite identities involving Pochhammer and - Pochhammer symbols obtained via analytical methods
Paweł J. Szabłowski
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…
On a class of bivariate distributions built of q-ultraspherical polynomials
Paweł J. Szabłowski
Our primary result concerns the positivity of specific kernels constructed using the -ultraspherical polynomials. In other words, it concerns a two-parameter family of bivariate…
Applications of infinite lower triangular matrices and their group structure in combinatorics and the theory of orthogonal polynomials
Paweł J. Szabłowski
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…
Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths
Paweł J. Szabłowski
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are importan…