The beta-function formalism is being used to study the constant-roll inflation in k-essence models. Assuming the second slow-roll parameter as a constant leads to a first-order differential equation for $\beta$-function which much easier to solve and find a solution than the second (non-linear) order equation that we have in the corresponding standard constant-roll inflation. Many cosmological models are known as a subclass of k-essence, so we will try to consider the model as general as possible. It is determined that the second slow-roll parameter should be positive to produce a small value for the first slow-roll parameter. The scenario is considered for three well-known cosmological models, and it is clarified that for the non-canonical and tachyon model, the scalar spectral index never reaches the observational range, however for the DBI model we could arrive as a result consistent with the observational data.

β函数形式主义被用于研究k本质模型中的恒定侧倾充气。假设第二个慢滚参数为常数，则导致一阶微分方程为$\beta$-函数，它比相应的标准恒定侧倾充气中的二阶（非线性）方程更容易求解和找到解决方案。许多宇宙学模型被称为k本质的子类，因此我们将尝试考虑该模型尽可能通用。确定第二慢滚动参数应为正，以使第一慢滚动参数产生较小的值。针对三种著名的宇宙学模型考虑了该场景，并明确了对于非正则和极谱模型，标量光谱指数从未达到观测范围，但是对于DBI模型，我们可以得出的结果与观测数据。