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In this article we prove that the gamma factors attached to genericrepresentations of ${\rm U}_{2n+1}\times{\rm Res}_{E/F}{\rm GL}_r$ over a localfield $F$ defined by various approaches coincide when $F$ is non-archimedeanand under additional assumptions on $n,r$ and $E$ when $F$ is archimedean.

On gamma factors of generic representations of ${\rm U}_{2n+1}\times{\rm Res}_{E/F}{\rm GL}_r$