∫-11ⅇ-(x+1)⁢z⁢Pn(α,β)⁡(x)⁢(1-x)α⁢(1+x)β⁢ⅆ⁡x=(-1)n⁢2α+β+n+1⁢Γ⁡(α+n+1)⁢Γ⁡(β+n+1)Γ⁡(α+β+2⁢n+2)⁢n!⁢zn⁢F11⁡(β+n+1α+β+2⁢n+2;-2⁢z),