DLMF:18.14.E20 (Q5685): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1qdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1sdec

Latest revision as of 15:36, 2 January 2020

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DLMF:18.14.E20
No description defined

    Statements

    Defining formula
    | P n ( α , β ) ⁡ ( x n , n - m ) P n ( α , β ) ⁡ ( 1 ) | > | P n + 1 ( α , β ) ⁡ ( x n + 1 , n - m + 1 ) P n + 1 ( α , β ) ⁡ ( 1 ) | , Jacobi-polynomial-P 𝛼 𝛽 𝑛 subscript 𝑥 𝑛 𝑛 𝑚 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 subscript 𝑥 𝑛 1 𝑛 𝑚 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 1 1 {\displaystyle{\displaystyle\left|\frac{P^{(\alpha,\beta)}_{n}\left(x_{n,n-m}% \right)}{P^{(\alpha,\beta)}_{n}\left(1\right)}\right|>\left|\frac{P^{(\alpha,% \beta)}_{n+1}\left(x_{n+1,n-m+1}\right)}{P^{(\alpha,\beta)}_{n+1}\left(1\right% )}\right|,}}
    0 references
    DLMF id
    DLMF:18.14.E20
    0 references
    constraint
    m = 1 , 2 , … , n 𝑚 1 2 … 𝑛 {\displaystyle{\displaystyle m=1,2,\dots,n}}
    0 references
    Symbols used
    Q11660
    Defining formula
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2agdec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1edec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1qdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1sdec
    0 references
     
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