I have to find the value of this integral: $\int_{-1}^1 \ln(1-x)*P_3(x)\,dx$
where $P_3(x)$ is the Legendre polynomial.
I thought I can write $\ln(1-x)$ as a summation of Legendre polynomials and then use the orthogonality relation to find the answer. That didn't really work, the closest I got was to:
$\ln(1-x)$=$\sum_{n=1}^\infty P_n(1)*x^n$ and that's not getting me anywhere.
Is this the right track of thought? Or is this question done in an entirely different method?
P.S The answer is $\frac {-1}6$