Integral Formulas for Hermite-Based Peters-Type Simsek Polynomials and Their Applications

Integrals and derivatives serve as fundamental instruments across virtually all scientific disciplines. Due to their extensive application, researchers have consistently sought to develop novel identities and formulas for both operations. This study aims to introduce several new integral formulas involving Hermite-based Peters-type Simsek polynomials, alongside their associated functions. These results establish connections with logarithmic functions and various special sequences, including bivariate Hermite polynomials and Peters-type Simsek numbers. Additionally, the paper provides insightful remarks and observations regarding the finding.