On a q‐Laplace–type integral operator and certain class of series expansion

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Abstract
In this paper, we develop a q‐theory of the q‐Laplace–type integral operators qL2 and ql2 introduced by Uçar and Albayrak in 2011. We derive several identities and establish various results related to the q‐Laplace–type integral operators of various classes of q‐special functions and q‐series expansions. By using a q‐series representation of the q‐analogues, we obtain results enfolding power series of even orders. Further, by utilizing the new results, we obtain formulas and conclusions associated with q‐hypergeometric functions of first and second types. In a brief reading, we finally establish new formulas involving q‐trigonometric and q‐Bessel functions as well.

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