∫x(1-x2)3/2⁢Pνμ⁡(x)⁢Qνμ⁡(x)⁢ⅆ⁡x=1(1-4⁢μ2)⁢(1-x2)1/2⁢((1-2⁢μ2+2⁢ν⁢(ν+1))⁢Pνμ⁡(x)⁢Qνμ⁡(x)+(2⁢ν+1)⁢(μ-ν-1)⁢x⁢(Pνμ⁡(x)⁢Qν+1μ⁡(x)+Pν+1μ⁡(x)⁢Qνμ⁡(x))+2⁢(μ-ν-1)2⁢Pν+1μ⁡(x)⁢Qν+1μ⁡(x)),