DLMF:18.9.E16

MaRDI QIDQ6309

• Label: DLMF:18.9.E16

Digital Library of Mathematical Functions ID 18.9.E16

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

Symbols List

• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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