SOME IDENTITIES INVOLVING THE LEGENDRE'S CHI-FUNCTION

Some identities involving the near pseudo Smarandache function

For any positive integer n and fixed integer t ≥ 1, we define function Ut(n) = min{k : 1 t + 2 t + · · · + n t + k = m, n | m, k ∈ N + , t ∈ N + }, where n ∈ N + , m ∈ N + , which is a new pseudo Smarandache function. The main purpose of this paper is using the elementary method to study the properties of Ut(n), and obtain some interesting identities involving function Ut(n). In reference [1], ...

Some Remarkable Identities Involving Numbers

The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers. Formulas for short multiplication are sometimes referred in English or French as remarkable identities. The same formulas could be found in works conce...

Combinatorial Identities Involving the Möbius Function

We derive some identities and inequalities concerning the Möbius function. Our main tool is phi functions for intervals of positive integers and their unions.

Some More Identities Involving Rational Sums

The representation of sums in closed form can in some cases be achieved through a variety of different methods, including transform techniques, W–Z methods, Riordan arrays and integral representations. The interested reader is referred to the works of Egorychev [2], Gould [3], Merlini, Sprugnoli and Verri [4], Petkovšek, Wilf and Zeilberger [5] and Sofo [6], [7] and [8]. Recently Diaz-Barrero e...

Some identities involving generalized Gegenbauer polynomials