Abstract

In this article, we investigate a three classes of generalized mixed type double Bernoulli-Gegenbauer-Gould and Hopper (BGG-H) polynomials. Some special polynomials of the generalized mixed type Bernoulli-Gegenbauer polynomials are discussed to obtain certain results and relations of our double (BGG-H) polynomials in terms of known and unknown functions.~Some inequalities and limiting cases of double (BGG-H) polynomials are presented and then on using them we construct a matrix representation and obtain integral estimates.

Keywords and Phrases

Bernoulli's polynomials, Gegenbauer polynomials, Gould and Hopper's polynomials, double Bernoulli-Gegenbauer-Gould and Hopper polynomials, matrix representations, integral estimates.

A.M.S. subject classification

11B83, 11C08, 33B10, 33B99.

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