  New quantal states which interpolate between the coherent states of the
Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states
are obtained as the coherent states of a closed and symmetric algebra which
interpolates between the two algebras. The overcompleteness of the
interpolating coherent states is established. Differential operator
representations in suitable spaces of entire functions are given for the
generators of the algebra. A nonsymmetric set of operators to realize the
Heisenberg-Weyl algebra is provided and the relevant coherent states are
studied.
