Related papers: Comment on `A general integral identity'

In this paper, a new identity for convex functions is derived. A consequence of the identity is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in…

In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.

Recently the second named author discovered a combinatorial identity in the context of vertex representations of quantum Kac-Moody algebras. We give a direct and elementary proof of this identity. Our method is to show a related identity of…

This paper builds on the research initiated by Boyadzhiev, but introduces generalized harmonic numbers, \[ H_n(\alpha)= \sum_{k=1}^n \frac{\alpha^{k}}{k}, \] which enable the derivation of new identities as well as the reformulation of…

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.

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…

We present a simple proof and a generalization of a Menon-type identity by Li, Hu and Kim, involving Dirichlet characters and additive characters.

We present two proofs each, all shorter than the original proofs, of two elegant combinatorial identities that came up in the beautiful article arXiv:2010.00077 .

In this paper we establish a suprising fundamental identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]

In this paper, an integral identity for twice differentiable functions is generalized. Then, by using convexity of |f''| or q-th power of |f''| and with the aid of power mean and Holder's inequalities we achieved some new results. We also…

We give new, short proofs of the presentations for the partition monoid and its singular ideal originally given in the author's 2011 papers in J Alg and IJAC.

We develop the Denef-Loeser motivic integration to the equivariant motivic integration and use it to prove the full integral identity conjecture for regular functions.

We discuss an algebraic identity, due to Sylvester, as well as related algebraic identities and applications.

We provide bijective proofs of two classic identities that are very simple to prove using generating functions, but surprisingly difficult to prove combinatorially. The problem of finding a bijective proof for the first identity was first…

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…

In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…

We find this identity, that looks like an exercise in Calculus 1, surprising, and beautiful. We hope that you would too.

A generalization of the Chu-Vandermonde convolution is presented and proved with the integral representation method. This identity can be transformed into another identity, which has as special cases two known identities. Another identity…