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We reexamine and extend a group of solutions in series of Bessel functionsfor a limiting case of the confluent Heun equation and, then, apply suchsolutions to the one-dimensional Schr\"odinger equation with an invertedquasi-exactly solvable potential as well as to the angular equation for anelectron in the field of a point electric dipole. For the first problem we findfinite- and infinite-series solutions which are convergent and bounded for anyvalue of the independent variable. For the angular equation, we also findexpansions in series of Jacobi polynomials.

A limit of the confluent Heun equation and the Schrödinger equation for an inverted potential and for an electric dipole