Conformal mappings from annuli to canonical doubly connected Bell representations

This paper derives formulae, expressed in terms of Schottky–Klein prime functions, for the conformal mapping between concentric annuli and Bell representations which are canonical doubly connected planar domains. New formulae relating the conformal moduli associated with the two respective canonical domains are derived and complement recent results by Jeong, Oh and Taniguchi [M. Jeong, J.-W. Oh, M. Taniguchi, Equivalence problem for annuli and Bell representations in the plane, J. Math. Anal. Appl. 325 (2007) 1295–1305].