\[\int_{0}^{x}t^{\alpha}\frac{L^{(\alpha)}_{m}\left(t\right)}{L^{(\alpha)}_{m}%
\left(0\right)}(x-t)^{\beta}\frac{L^{(\beta)}_{n}\left(x-t\right)}{L^{(\beta)}%
_{n}\left(0\right)}\,\mathrm{d}t=\frac{\Gamma\left(\alpha+1\right)\Gamma\left(%
\beta+1\right)}{\Gamma\left(\alpha+\beta+2\right)}x^{\alpha+\beta+1}\frac{L^{(%
\alpha+\beta+1)}_{m+n}\left(x\right)}{L^{(\alpha+\beta+1)}_{m+n}\left(0\right)}.\]