  We review the series solutions of the general and single-confluent Heun
equations in terms of powers, ordinary-hypergeometric and
confluent-hypergeometric functions. The conditions under which the expansions
reduce to finite sums as well as the cases when the coefficients of
power-series expansions obey two-term recurrence relations are discussed.
Infinitely many cases for which a solution of a general or single-confluent
Heun equation is written through a single generalized hypergeometric function
are indicated. It is shown that the parameters of this generalized
hypergeometric function are the roots of a certain polynomial equation, which
we explicitly present for any given order.
