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We give an overview of known properties of the Mellin transform F(s) of the product of generalized hypergeometric functions 0 F 1 [-a 2 x 2 ] 1 F 2 [-b 2 x 2 ] for a>0 and b>0. In particular, we derive a new representation for F(s) that is valid in both the critical and supercritical cases where a=b.
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