We construct a new family of boson coherent states using a specially design
ed function which is a solution of a functional equation d epsilon(q, x)/dx
= epsilon(q, qx) with 0 less than or equal to q less than or equal to 1 an
d epsilon(q, 0) = 1. We use this function in place of the usual exponential
to generate new coherent states \q, z] from the vacuum, which are normaliz
ed and continuous in their label z. These states allow the resolution of un
ity, and a corresponding weight function is furnished by the exact solution
of the associated Stieltjes moment problem. They also permit exact evaluat
ion of matrix elements of an arbitrary polynomial given as a normally-order
ed function of boson operators. We exemplify this by showing that the photo
n number statistics for these states is sub-Poissonian. For any q < 1 the s
tates \q, z] are squeezed; we obtain and discuss their signal to quantum no
ise ratio. The function e( q, x) allows a natural generation of multiboson
coherent states of arbitrary multiplicity, which is impossible for the usua
l coherent states. For q = 1 all the above results reduce to those for conv
entional coherent states. Finally, we establish a link with q-deformed boso
ns. (C) 1999 American Institute of Physics. [S0022-2488(99)01404-8].