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In this paper, the basic analogue of the Laplace transforms involving the product of a general class of q-polynomials along with q-analogue of Fox's H-function and q-analogue of I-function is evaluated. Limiting cases of the main outcomes are also evaluated. The paper shows a large variety of outcomes that can be achieved. [ABSTRACT FROM AUTHOR]

In this article, the general polynomials are taken as base with the Gould-Hopper matrix polynomials to introduce a family of 3-variable general-Gould-Hopper matrix polynomials (3VgGHMaP). These polynomials are framed within the context of monomiality principle and their properties are established. Examples of some members belonging to this family are considered. Certain bilateral and bilinear generating matrix functions for 3Vg-GHMaP are also derived. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly defined (q, r,w)- Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q,r,w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w. [ABSTRACT FROM AUTHOR]