cos(νπ)Pνμ(x)=2νπ1/2xνμ(x21)μ/2Γ(ν+μ+1)𝐅(12μ12ν,12μ12ν+12;12ν;1x2)π1/2(x21)μ/22ν+1Γ(μν)xν+μ+1𝐅(12ν+12μ+1,12ν+12μ+12;ν+32;1x2),