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We obtain kernel functions associated with the quantum relativistic Todasystems, both for the periodic version and for the nonperiodic version with itsdual. This involves taking limits of previously known results concerning kernelfunctions for the elliptic and hyperbolic relativistic Calogero-Moser systems.We show that the special kernel functions at issue admit a limit that yieldsgenerating functions of B\"acklund transformations for the classicalrelativistic Calogero-Moser and Toda systems. We also obtain thenonrelativistic counterparts of our results, which tie in with previous resultsin the literature.

Kernel functions and B\"acklund transformations for relativistic Calogero-Moser and Toda systems