DLMF:18.9.E5 (Q5601): Difference between revisions

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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.m1ddec

Latest revision as of 15:22, 2 January 2020

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DLMF:18.9.E5
No description defined

    Statements

    Defining formula
    ( 2 ⁢ n + α + β + 1 ) ⁢ P n ( α , β ) ⁡ ( x ) = ( n + α + β + 1 ) ⁢ P n ( α , β + 1 ) ⁡ ( x ) + ( n + α ) ⁢ P n - 1 ( α , β + 1 ) ⁡ ( x ) , 2 𝑛 𝛼 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 𝑛 𝛼 𝛽 1 Jacobi-polynomial-P 𝛼 𝛽 1 𝑛 𝑥 𝑛 𝛼 Jacobi-polynomial-P 𝛼 𝛽 1 𝑛 1 𝑥 {\displaystyle{\displaystyle(2n+\alpha+\beta+1)P^{(\alpha,\beta)}_{n}\left(x% \right)=(n+\alpha+\beta+1)P^{(\alpha,\beta+1)}_{n}\left(x\right)+(n+\alpha)P^{% (\alpha,\beta+1)}_{n-1}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.9.E5
    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.m2abdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
    0 references
     
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