∫-11(1-x)α⁢(1+x)β⁢Pn(α,β)⁡(x)⁢ⅇⅈ⁢x⁢y⁢ⅆ⁡x=(ⅈ⁢y)n⁢ⅇⅈ⁢yn!⁢2n+α+β+1⁢B⁡(n+α+1,n+β+1)⁢F11⁡(n+α+1;2⁢n+α+β+2;-2⁢ⅈ⁢y).