The q-Exponential Operator and the Bivariate Carlitz Polynomial with Numerical Applications
DOI:
https://doi.org/10.32792/jeps.v10i2.84الكلمات المفتاحية:
The q-exponential operator، generating function، symmetry property، Mehler’s formula، Rogers formula، linearization formula، extended generating functionالملخص
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.المراجع
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