The Basic and Extended Identities for Certain q-Polynomials | ||
| Journal of College of Education for Pure Science | ||
| Article 1, Volume 2, Issue 2, June 2012, Pages 10-21 | ||
| Author | ||
| Mohammed A. Abdlhusein | ||
| Abstract | ||
| In this paper, we introduce the generating function, Mehler’s formula, Roger’s formula, the linearization formula and the inverse relation of the linearization formula of the polynomials G_n (x;q), which is defined by L.Carlitz [3]. Also we introduce an extension of the generating function and extension of the Roger’s formula, the extended generating function of G_n (x;q) involves a 2ϕ1 sum and the extended Rogers formula involves a 3ϕ2 sum. All identities will be derived depending on the roles of the exponential operator E(θ) after representing the polynomials G_n (x;q) by this operator. | ||
| Keywords | ||
| The exponential operator; generating function; Mehler; Rogers formula; linearization formula; extended generating function; extended Rogers formula | ||
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