an=n!⁢(2⁢n+α+β+1)⁢Γ⁡(n+α+β+1)2α+β+1⁢Γ⁡(n+α+1)⁢Γ⁡(n+β+1)⁢∫-11f⁡(x)⁢Pn(α,β)⁡(x)⁢(1-x)α⁢(1+x)β⁢ⅆ⁡x.