  The Heisenberg algebra is first deformed with the set of parameters ${q, l,
\lambda}$ to generate a new family of generalized coherent states. In this
framework, the matrix elements of relevant operators are exactly computed. A
proof on sub-Poissonian character of the statistics of the main deformed states
is provided. This property is used to determine a generalized metric.
  A unified method of calculating structure functions from commutation
relations of deformed single-mode oscillator algebras is then presented. A
natural approach to building coherent states associated to deformed algebras is
deduced. Known deformed algebras are given as illustration.
  Futhermore, we generalize a class of two-parameter deformed Heisenberg
algebras related to meromorphic functions, called ${\cal R}(p,q)$-deformed
algebra. Relevant families of coherent states maps are probed and their
corresponding hypergeometric series are computed. The latter generalizes known
hypergeometric series and gives to a generalization of the binomial theorem.
  The involved notions of differentiation and integration generalize the usual
$q$- and $(p,q)$-differentiation and integration. A Hopf algebra structure
compatible with the ${\cal R}(p,q)$-algebra is deduced.
  We succeed in giving a new characterization of Rogers- Szeg\"o polynomials,
called ${\cal R}(p,q)$-deformed Rogers-Szeg\"o polynomials, by their three-term
recursion relations and the associated quantum algebra built with corresponding
creation and annihilation operators. Continuous ${\cal R}(p,q)$-deformed
Hermite polynomials and their recursion relation are also deduced. Novel
algebraic relations are provided and discussed. The whole formalism is
performed in a unified way, generalizing known relevant results which are
straightforwardly derived as particular cases.
