Glasnik Matematicki, Vol. 53, No. 1 (2018), 9-31.

SOME RESULTS ON q-HERMITE BASED HYBRID POLYNOMIALS

Mumtaz Riyasat and Subuhi Khan

Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India
e-mail: mumtazrst@gmail.com
e-mail: subuhi2006@gmail.com

Abstract.   In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Euler polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Further, the 2D q-Hermite based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials are introduced and important relations for these polynomials are also established. Finally, a new class of the 2D q-Hermite based Appell polynomials is investigated as the generalization of the above polynomials. The determinant definitions for the 2D q-Hermite based Appell and related polynomials are also explored.

2010 Mathematics Subject Classification.   11B73, 11B83, 11B68.

Key words and phrases.   q-Hermite type polynomials, Apostol type q-Frobenius-Euler polynomials, q-Hermite based Apostol type Frobenius-Euler polynomials.


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DOI: 10.3336/gm.53.1.02


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