DLMF:18.17.E47 (Q5788)

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Language	Label	Description	Also known as
English	DLMF:18.17.E47	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\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)}.}}

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DLMF:18.17.E47

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2ardec

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Defining formula

{\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r12.m2ajdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aatdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aardec

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Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1ddec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1atdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1ardec

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