Kucukoglu, Irem2026-01-242026-01-242023https://hdl.handle.net/20.500.12868/4747The main aim of this study is to investigate the multiparametric higher-order Hermite-based Peters-type Simsek numbers and polynomials of the first kind, which were introduced by the author in her recent paper [18]. To achieve this aim, we first provide pseudocodes for symbolic computation of these numbers and polynomials. Moreover, we implement these pseudocodes in the Wolfram language. By these implementations, we provide some tables and plots regarding these numbers and polynomials in some arbitrarily chosen special cases. By using their generating functions with their functional equations, we derive some finite sums, identities and derivative formulas concerning these numbers and polynomials. We also investigate the first order multiparametric Hermite-based Peters-type Simsek polynomials and we provide some remarks and observations about their some reductions. Fi-nally, we conclude the paper by providing some remarks and open problems on the potential applications that could emerge from the Sheffer-type sequences, the heat-type equations, the orthogonality and the analytic continuation. © 2023, MTJPAM Turkey. All rights reserved.eninfo:eu-repo/semantics/closedAccess05A1005A1511B8333C4535K0565D20Article511021232-s2.0-85172698386Q1