DLMF:18.14.E3

MaRDI QIDQ6363

• Label: DLMF:18.14.E3

Digital Library of Mathematical Functions ID 18.14.E3

${\displaystyle{\displaystyle\left(\tfrac{1}{2}(1-x)\right)^{\frac{1}{2}\alpha+\frac{1}{4}}\left(\tfrac{1}{2}(1+x)\right)^{\frac{1}{2}\beta+\frac{1}{4}}|P^{(\alpha,\beta)}_{n}\left(x\right)|\leq\frac{\Gamma\left(\max(\alpha,\beta)+n+1\right)}{\pi^{\frac{1}{2}}n!\left(n+\tfrac{1}{2}(\alpha+\beta+1)\right)^{\max(\alpha,\beta)+\frac{1}{2}}},}}$

Constraint(s)

${\displaystyle{\displaystyle-\tfrac{1}{2}\leq\beta\leq\tfrac{1}{2}}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$: Jacobi polynomial
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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