DLMF:18.17.E13 (Q5754)

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Language	Label	Description	Also known as
English	DLMF:18.17.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{x^{\frac{1}{2}n}(x-1)^{\lambda+\mu-\frac{1}{% 2}}}{\Gamma\left(\lambda+\mu+\tfrac{1}{2}\right)}\frac{C^{(\lambda+\mu)}_{n}% \left(x^{-\frac{1}{2}}\right)}{C^{(\lambda+\mu)}_{n}\left(1\right)}=\int_{1}^{% x}\frac{y^{\frac{1}{2}n}(y-1)^{\lambda-\frac{1}{2}}}{\Gamma\left(\lambda+% \tfrac{1}{2}\right)}\frac{C^{(\lambda)}_{n}\left(y^{-\frac{1}{2}}\right)}{C^{(% \lambda)}_{n}\left(1\right)}\frac{(x-y)^{\mu-1}}{\Gamma\left(\mu\right)}% \mathrm{d}y,}}

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DLMF:18.17.E13

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{\displaystyle{\displaystyle x>1}}

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Defining formula

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

C5.S2.E1.m2aedec

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Defining formula

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

C1.S4.SS4.m1aldec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aldec

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Defining formula

{\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

C18.S3.T1.t1.r3.m2abdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1hdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1ldec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1jdec

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