DLMF:18.14#Ex4 (Q5682)

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DLMF:18.14#Ex4
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    Statements

    Defining formula
    | P n ( α , β ) ⁡ ( x n , n ) | < | P n ( α , β ) ⁡ ( x n , n - 1 ) | < ⋯ < | P n ( α , β ) ⁡ ( x n , m + 1 ) | , Jacobi-polynomial-P 𝛼 𝛽 𝑛 subscript 𝑥 𝑛 𝑛 Jacobi-polynomial-P 𝛼 𝛽 𝑛 subscript 𝑥 𝑛 𝑛 1 ⋯ Jacobi-polynomial-P 𝛼 𝛽 𝑛 subscript 𝑥 𝑛 𝑚 1 {\displaystyle{\displaystyle|P^{(\alpha,\beta)}_{n}\left(x_{n,n}\right)|<|P^{(% \alpha,\beta)}_{n}\left(x_{n,n-1}\right)|<\cdots<|P^{(\alpha,\beta)}_{n}\left(% x_{n,m+1}\right)|,}}
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    DLMF id
    DLMF:18.14#Ex4
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    constraint
    - 1 < α < - 1 2 , - 1 < β < - 1 2 . formulae-sequence 1 𝛼 1 2 1 𝛽 1 2 {\displaystyle{\displaystyle-1<\alpha<-\tfrac{1}{2},-1<\beta<-\tfrac{1}{2}.}}
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