On multiple integral relations involving generalized Mellin-Barnes type of contour integral

In this paper, we first evaluate two finite basic integrals involving the product of the multivariable polynomial S ^h1 _L ^,··· ^,hr [x ₁ ^,··· ^,x _r] and two generalized Mellin Barnes type of contour integrals. Next, with the help of these basic integrals we establish two integral relations which involve general arguments and are the most general in nature. Again by suitably specializing the function f in the first integral relation, we have evaluated a multiple integral which is new and quite general in nature. Finally, we present four special cases of our main findings involving the _pψ _q(z), J ^ν,μ _λ (z) and S ^h _L [x], which are also believed to be new. Some known results follow as special cases of our findings.