The connection between convergence of product integration rules and mean convergence of Lagrange interpolation in L, (1 <p < 00) has been thoroughly analysed by Sloan and Smith [37]. Motivated byâ€¦ (More)

This paper deals with Carlitz compositions of natural numbers (adjacent parts have to be different). The following parameters are analysed: number of parts, number of equal adjacent parts in ordinaryâ€¦ (More)

For words of length n, generated by independent geometric random variables, we consider the mean and variance, and thereafter the distribution of the number of runs of equal letters in the words. Inâ€¦ (More)

An algorithm is considered, and shown to lead to various unusual and unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by theâ€¦ (More)

The idea of graph compositions generalizes both ordinary compositions of positive integers and partitions of finite sets. In this paper we develop formulas, generating functions, and recurrenceâ€¦ (More)

Archibald and Knopfmacher recently considered the largest missing value in a composition of an integer and established the mean and variance. Our alternative, probabilistic approach produces (inâ€¦ (More)

The q-Engel Expansion is an algorithm that leads to unique series expansions of qseries. Various examples related to classical partition theorems, including the RogersRamanujan identities togetherâ€¦ (More)