DLMF:18.14.E3 (Q5666): Difference between revisions

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Property / constraint
 

- 1 2 ≤ β ≤ 1 2 1 2 𝛽 1 2 {\displaystyle{\displaystyle-\tfrac{1}{2}\leq\beta\leq\tfrac{1}{2}}}

-\tfrac{1}{2}\leq\beta\leq\tfrac{1}{2}
Property / constraint: - 1 2 ≤ β ≤ 1 2 1 2 𝛽 1 2 {\displaystyle{\displaystyle-\tfrac{1}{2}\leq\beta\leq\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 17:00, 30 December 2019

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DLMF:18.14.E3
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    Statements

    test
    ( 1 2 ⁢ ( 1 - x ) ) 1 2 ⁢ α + 1 4 ⁢ ( 1 2 ⁢ ( 1 + x ) ) 1 2 ⁢ β + 1 4 ⁢ | P n ( α , β ) ⁡ ( x ) | ≤ Γ ⁡ ( max ⁡ ( α , β ) + n + 1 ) π 1 2 ⁢ n ! ⁢ ( n + 1 2 ⁢ ( α + β + 1 ) ) max ⁡ ( α , β ) + 1 2 , superscript 1 2 1 𝑥 1 2 𝛼 1 4 superscript 1 2 1 𝑥 1 2 𝛽 1 4 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 Euler-Gamma 𝛼 𝛽 𝑛 1 superscript 𝜋 1 2 𝑛 superscript 𝑛 1 2 𝛼 𝛽 1 𝛼 𝛽 1 2 {\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}}},}}
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    DLMF id
    DLMF:18.14.E3
    0 references
    constraint
    - 1 2 ≤ β ≤ 1 2 1 2 𝛽 1 2 {\displaystyle{\displaystyle-\tfrac{1}{2}\leq\beta\leq\tfrac{1}{2}}}
    0 references
     
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