Related papers: Generalization of the Taylor formula

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…

The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the…

In the present paper we introduce old and new results related to St\"ormer theorem about Pell equations. Moreover we give four types of applications of these results.

Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for…

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…

The paper presents the generalized persistency of excitation conditions. They are not only valid for much broader range of applications than their classical counterparts but also elegantly prove the validity of the latter. The novelty and…

The Lie algebras expansion method is used to show that the Maxwell (super)algebras and some of their generalizations can be derived in a simple way as particular expansions of o(3,2) and osp(N|4).

It is shown how the well-known large mass expansion can be simplified to obtain more terms of the expansion in an analytic form. Expanding two-loop four-point Feynman integrals which contribute to the process $H \to ggg$ is used as an…

This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.

The Flavour Expansion Theorem, which has been recently proposed as a more general and elegant algebraic method, for the derivation of the commonly used Mass Insertion Approximation, is revisited. The theorem is reviewed, with respect to its…

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.

In this paper, we derive an optimal first-order Taylor-like formula. In a seminal paper [14], we introduced a new first-order Taylor-like formula that yields a reduced remainder compared to the classical Taylor's formula. Here, we relax the…

Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…

The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…