Some identities on generalized harmonic numbers and generalized harmonic functions

TL;DR

This paper derives new identities involving generalized harmonic numbers and functions using elementary methods, highlighting their importance in combinatorics, number theory, and algorithm analysis.

Contribution

It introduces novel identities connecting generalized harmonic numbers and functions through elementary derivations from beta functions.

Findings

Derived identities involving generalized harmonic numbers and functions.

Showed applications in combinatorics and number theory.

Provided elementary proofs for complex relations.

Abstract

The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms. The aim of this paper is to derive some identities involving generalized harmonic numbers and generalized harmonic functions from the beta functions F(x)= B( x+1, n+1), ( n=0,1,2,..) using elementary methods.