  In this article, we prove the transformation formula for the reduced Bergman
kernels under proper holomorphic correspondences between bounded domains in the
complex plane. As a corollary, we obtain the transformation formula for the
reduced Bergman kernels under proper holomorphic maps. We also establish the
transformation formula for the weighted reduced Bergman kernels under proper
holomorphic maps. Finally, we provide an application of this transformation
formula.
