DLMF:18.9.E18 (Q5614)

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Language	Label	Description	Also known as
English	DLMF:18.9.E18	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(2n+\alpha+\beta+2)(1-x^{2})\frac{\mathrm{d}}{% \mathrm{d}x}P^{(\alpha,\beta)}_{n}\left(x\right)=(n+\alpha+\beta+1)\left(% \alpha-\beta+(2n+\alpha+\beta+2)x\right)P^{(\alpha,\beta)}_{n}\left(x\right)-2% (n+1)(n+\alpha+\beta+1)P^{(\alpha,\beta)}_{n+1}\left(x\right).}}

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DLMF:18.9.E18

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Defining formula

{\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2agdec

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derivative of $$f$$ with respect to $$x$$

Defining formula

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

C1.S4.E4.m2acdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1rdec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1qdec

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