# Integral of Legendre's first kind function of degree $-1/2+il$

Let $$l=-1/2+i\,t$$; $$t\in\mathbb{R}$$. I'm wondering if there is a way to compute the following integral $$\int_{-1}^xP^m_l(\gamma)^2 \,d\,\gamma; -1 In which $$P^m_l$$ is the Legendre's first kind function of degree $$l=-1/2+it$$ and of order $$m\in\mathbb{N}$$.