Related papers: An identity for derivatives

The generalized second-order partial derivatives of 1/r, where r is the radial distance in 3D, are obtained using a result of the potential theory of classical analysis. Some non-spherical regularization alternatives to the standard…

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

We generalize Menon's identity by considering sums representing arithmetical functions of several variables. As an application, we give a formula for the number of cyclic subgroups of the direct product of several cyclic groups of arbitrary…

We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.

Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…

In this paper we generalize the famous Jacobi's triple product identity, considered as an identity for theta functions with characteristics and their derivatives, to higher genus/dimension. By applying the results and methods developed in…

We give explicit formulae and study the combinatorics of an identity holding in all Rota-Baxter algebras. We describe the specialization of this identity for a couple of examples of Rota-Baxter algebras.

We prove the formula for the second order "thick" distributional derivative of 1/r in 3 dimensional Euclidean space. This formula generalizes the well known Frahm formulas for the distributional derivatives of 1/r.

A generalized Liouville-Jacobi Identity is proved for the determinant $\det{X(t)}$ of a solution $X(t)$ to the linear nonhomogeneous first-order matrix differential equation with left- and right-coefficient matrices $\ \frac{{\rm d}}{{\rm…

In this paper, we give corrected and improved definitions of the sets $S$ and $\Delta$ compared to [1]. By using these new definitions, we go throughout the proof of the main result in [1], and we correct it.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

In this paper we give new identities involving q-Euler polynomials of higher order.

We generalize the Li-Yau inequality for second derivatives and we also establish Li-Yau type inequality for fourth derivatives. Our derivation relies on the representation formula for the heat equation.

We introduce signature payoffs, a family of path-dependent derivatives that are given in terms of the signature of the price path of the underlying asset. We show that these derivatives are dense in the space of continuous payoffs, a result…

The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular…

A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…

This work revolves around the study of differentiability in the Stieltjes sense of a product of functions. A formula for the first order derivative has been obtained in the past, which is similar to the usual one with some extra terms in…

In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…

We prove some new formulae for the derivatives of the generalized Gegenbauer polynomials associated to the Lie algebra $A_2$.

We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set.