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is done along the vertical line thatlies entirely within the overlap of the (suitable transformed) fundamental strips.

We can replace by . This gives following alternative form of the theorem:Let and be functions with well-defined Mellin transforms in the fundamental strips .Let with and choose with . If the functions and are also square-integrable over the interval , then we have

We can replace by .This gives following theorem:Let be a function with well-defined Mellin transform in the fundamental strip .Let with

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