DLMF:18.14.E2 (Q5665)

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DLMF:18.14.E2
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    Statements

    Defining formula
    | P n ( α , β ) ⁡ ( x ) | ≤ | P n ( α , β ) ⁡ ( - 1 ) | = ( β + 1 ) n n ! , Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 Pochhammer 𝛽 1 𝑛 𝑛 {\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x\right)|\leq|P^{(% \alpha,\beta)}_{n}\left(-1\right)|=\frac{{\left(\beta+1\right)_{n}}}{n!},}}
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    DLMF id
    DLMF:18.14.E2
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    constraint
    β ≥ - 1 2 𝛽 1 2 {\displaystyle{\displaystyle\beta\geq-\tfrac{1}{2}}}
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