We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients \(z^n/\sqrt{n!}\) of the canonical coherent states by a specific generalized factorial \(x_n^{\gamma ,\sigma }!\) where parameters \(\gamma \) and \(\sigma \) satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut–Girardello coherent states and those of the philophase states. In the particular case of parameters \(\gamma \) and \(\sigma \), we attache these states to the pseudoharmonic oscillator depending on two parameters \(\alpha ,\beta > 0\). The obtained nonlinear coherent states are superposition of eigenstates of this oscillator. The associated Bargmann-type transform is defined and we derive some results.

通过用特定的广义阶乘\ {x_n ^ {\ gamma，\ sigma代替规范相干态的系数\（z ^ n / \ sqrt {n！} \）的阶乘，构造非线性相干态的两参数族}！\），其中参数\（\ gamma \）和\（\ sigma \）满足某些条件，可以验证归一化条件和身份解析。所获得的族是Barut-Girardello相干态和介相态的推广。在参数\（\ gamma \）和\（\ sigma \）的特殊情况下，我们根据两个参数\（\ alpha，\ beta> 0 \）将这些状态附加到伪谐波振荡器上。获得的非线性相干态是该振荡器的本征态的叠加。定义了相关的Bargmann型变换，我们得出了一些结果。