Some differentiation formulas for Legendre polynomials

In a series of recent works, we have provided a number of explicit expressions for the derivative of the associated Legendre function of the first kind with respect to its degree, $[\partial P_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$,with$m,n\in$\mathbb{N}$$. In this communication, we use some of those expressions to obtain several, we believe new, explicit formulas for the derivatives ${\mathrm{d}}^m[P_n(z)\ln (z\pm 1)]\mathrm{/}\mathrm{d}{z}^m$, where $P_n(z)$ is the Legendre polynomial.