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We construct two-parameters family of nonlinear coherent states by replacingthe factorial in coefficients $z^n/\sqrt{n!}$ of the canonical coherent statesby a specific generalized factorial $x_n^{\gamma,\sigma}!$ where parameters$\gamma$ and $\sigma$ satisfy some conditions for which the normalizationcondition and the resolution of identity are verified. The obtained family is ageneralization of the Barut-Girardello coherent states and those of thephilophase states. In the particular case of parameters $\gamma$ and $\sigma$,we attache these states to the pseudo-harmonic oscillator depending on twoparameters $\alpha,\beta> 0$. The obtained nonlinear coherent states aresuperposition of eigenstates of this oscillator. The associated Bargmann-typetransform is defined and we derive some results.

A set of nonlinear coherent states for the pseudoharmonic oscillator