GENERALIZED THREE CLASSES OF MIXED TYPE DOUBLE BERNOULLI- GEGENBAUER-GOULD AND HOPPER POLYNOMIALS

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.