Alwhishi,S.Adigüzel,R.S.Turan,M.Mathematics2024-07-052024-07-0520190978-179980136-8978-179980134-410.4018/978-1-7998-0134-4.ch0072-s2.0-85108329335https://doi.org/10.4018/978-1-7998-0134-4.ch007https://hdl.handle.net/20.500.14411/3909Discrete q-Hermite I polynomials are a member of the q-polynomials of the Hahn class. They are the polynomial solutions of a second order difference equation of hypergeometric type. These polynomials are one of the q-analogous of the Hermite polynomials. It is well known that the q-Hermite I polynomials approach the Hermite polynomials as q tends to 1. In this chapter, the orthogonality property of the discrete q-Hermite I polynomials is considered. Moreover, the orthogonality relation for the k-th order q-derivatives of the discrete q-Hermite I polynomials is obtained. Finally, it is shown that, under a suitable transformation, these relations give the corresponding relations for the Hermite polynomials in the limiting case as q goes to 1. © 2020, IGI Global.eninfo:eu-repo/semantics/closedAccess[No Keyword Available]Book Part135162