  We reexamine and extend a group of solutions in series of Bessel functions
for a limiting case of the confluent Heun equation and, then, apply such
solutions to the one-dimensional Schr\"odinger equation with an inverted
quasi-exactly solvable potential as well as to the angular equation for an
electron in the field of a point electric dipole. For the first problem we find
finite- and infinite-series solutions which are convergent and bounded for any
value of the independent variable. For the angular equation, we also find
expansions in series of Jacobi polynomials.
