I want to find analytical summation formulas for these type series of Legendre polynomials: $$\sum_{n=1}^{\infty}{\frac{1}{n}P_{n-1}(cos\phi)P_{n}(cos\theta)}$$ $$\sum_{n=1}^{\infty}{\frac{1}{n}P_{n+1}(cos\phi)P_{n}(cos\theta)}$$ $$\sum_{n=1}^{\infty}{\frac{1}{2n+1}P_{n-1}(cos\phi)P_{n}(cos\theta)}$$ $$\sum_{n=1}^{\infty}{\frac{1}{2n+1}P_{n+1}(cos\phi)P_{n}(cos\theta)}$$
I find some formulas in the page of http://functions.wolfram.com/Polynomials/LegendreP/23/02/, but no formula can be used directly, so I seek help here. Any advice and hint are appreciated! Thank you very much.