A systematic exposition of Sheffer polynomial sequences via determinantal form is given. A general linear interpolation problem related to Sheffer sequences is considered. It generalizes many known cases of linear interpolation. Numerical examples and conclusions close the paper. 1. The modern umbral calculus In the 1970s Rota and his collaborators [17,19,20] began to construct a completely rig...

In this article, we define a new operator by Appell polynomials. Primarily, some equations are obtained using the properties of Korovkin theorem. Later, convergence sequence that have defined has been proved and approximation results given theory.

Using a heuristic that relates Appell--Lerch functions to divergent partial theta one can expand Hecke-type double-sums in terms of functions. We give examples where the be used as guide evaluate analogous triple-sums or false

A class of fractional derivative operators (with the Appell hypergeometric function in the kernel) is used here to define a new subclass of analytic functions and a coefficient bound inequality is established for this class of functions. Also, an inclusion theorem for a class of fractional integral operators involving the Hardy space of analytic functions is proved. The concluding remarks brief...

When constraints are applied to mechanical systems, additional forces of constraint are produced that guarantee their satisfaction. The development of the equations of motion for constrained mechanical systems has been pursued by numerous scientists and mathematicians, like Appell @1#, Beghin @2#, Chetaev @3#, Dirac @4#, Gauss @5#, Gibbs @6#, and Hamel @7#. All these investigators have used as ...

Abstract Gibbs manifolds are images of affine spaces symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum physics, where they extend ubiquitous role toric geometry. The variety is zero locus all polynomials that vanish on manifold. We compute these show low-dimensional. Our theory applied to a wide range scenarios, including matri...

Many statistical applications require establishing central limit theorems for sums/integrals ST (h) = ∫ t∈IT h(Xt)dt or for quadratic forms QT (h) = ∫ t,s∈IT b̂(t − s)h(Xt,Xs)dsdt, where Xt is a stationary process. A particularly important case is that of Appell polynomials h(Xt) = Pm(Xt), h(Xt,Xs) = Pm,n(Xt, Xs), since the “Appell expansion rank” determines typically the type of central limit t...

This article aims to introduce degenerate hybrid type Appell polynomials HQm(u,v,w;η) and establishes their quasi-monomial characteristics. Additionally, a number of features these are established, including symmetric identities, implicit summation formulae, differential equations, series definition operational formalism.