The q-Exponential Operator and the Bivariate Carlitz Polynomial with Numerical Applications

  • Ahmed J. Hussein Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq
  • Mohammed A. Abdlhusein Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq
Keywords: The q-exponential operator, generating function, symmetry property, Mehler’s formula, Rogers formula, linearization formula, extended generating function

Abstract

          In this paper, we introduce two operator roles for the -exponential operator , we represent the bivariate Carlitz polynomial  by the  operator  to derive the generating function, symmetry property, Mehler’s formula, Rogers formula, linearization formula,  the inverse linearization formula, another Rogers-type formula. Also we give an extended generating function, extended Mehler’s formula  extended Rogers formula, and another extended identities for the bivariate Carlitz polynomial by using the roles of the -exponential operator . Finally, we test the convergence conditions of all identities given in this paper and their effect numerically.  

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Published
2021-02-18
Section
Articles