New Formulas and Connections Involving Euler Polynomials

Abstract

The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well as those of the Euler polynomials. In terms of the Euler polynomials, new formulas for the derivatives of various symmetric and non-symmetric polynomials, including the well-known classical orthogonal polynomials, are given. This leads to the deduction of several new connection formulas between various polynomials and the Euler polynomials. As an important application, new closed forms for the definite integrals for the product of various symmetric and non-symmetric polynomials with the Euler polynomials are established based on the newly derived connection formulas.

Biomass Higher Heating Value Estimation: A Comparative Analysis of Machine Learning Models

“…Polynomials are often used in regression models because they can approximate a variety of functions and describe complex patterns in data. In the context of regression, polynomials enable model flexibility as they can model non-linear relationships between variables [25]. The application of polynomial regression is particularly useful in situations where simple linear models do not provide sufficiently accurate predictions, making polynomial regression a powerful tool in data analysis and machine learning [26,27].…”