# Some Evaluations of Parametric Euler Type Sums of Harmonic Numbers

## TL;DR

This paper derives identities for Euler-related harmonic number sums, providing closed-form expressions involving harmonic numbers, binomial coefficients, and zeta functions, with applications to quadratic and cubic harmonic number products.

## Contribution

It introduces new identities for Euler sums and offers explicit closed-form representations involving harmonic numbers and special functions.

## Key findings

- Derived identities for Euler related sums.
- Closed-form expressions involving harmonic numbers and zeta functions.
- Analyzed products of quadratic and cubic harmonic numbers.

## Abstract

We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers, shifted harmonic numbers and Riemann zeta function with positive integer arguments. In particular we investigate products of quadratic and cubic harmonic numbers and reciprocal parametric binomial coefficients. Some illustrative special cases as well as immediate consequences of the main results are also considered.