Finite Mellin transform for $$(p,q)$$ and symmetric calculus

In this paper, we have introduced and studied finite $$(p,q)$$ -Mellin transform which extends the known theory of finite q-Mellin transform. Also, in this paper, we study finite $$(p,q)$$ -Mellin transform in the framework of symmetric calculus. This study is new even for the special case $$p=q$$ . In both the cases, we provide several basic properties, inversion formulas, the appropriate convolution product and the Parseval type relations.