  This paper adds a new variable y($\mu^{\prime}=y(\omega+m N^{\phi})$) to
extend the results of the classic paper. We exploit the properties of curve
integrals. When y is greater than a certain limit, the effective potential of
the equation has no pole, then there is no potential well outside the event
horizon, when $\sqrt{2(m^2)}/{ r^2_+}< \omega < m\varOmega_H$,so the BTZ black
hole was superradiantly stable at that time.
