  We prove an expansion formula for elliptic hypergeometric series. In the
$q$-case, when the nome $p=0$, it generalizes $q$-hypergeometric transformation
formulas due to Liu, and Wang and Ma, results that are used to derive
identities for Hecke-type series and transformations for false and mock-theta
functions. Our formula contains an arbitrary sequence as an argument, and is
thus flexible in the number of parameters it contains. As a result, we are able
to derive several transformation formulas for elliptic hypergeometric series,
as well as double summation formulas.
