Please have a look at the following paper
https://www.sciencedirect.com/science/article/pii/S0021904598932075
In particular, Eq. (6) to get the answer to your question.
Lohöfer, G., Inequalities for the associated Legendre functions, J. Approximation Theory 95, No. 2, 178-193 (1998). ZBL0923.33002.
