DLMF:18.9.E4 (Q5600)

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DLMF:18.9.E4
No description defined

    Statements

    Defining formula
    ( 1 - x ) ⁢ P n ( α + 1 , β ) ⁡ ( x ) + ( 1 + x ) ⁢ P n ( α , β + 1 ) ⁡ ( x ) = 2 ⁢ P n ( α , β ) ⁡ ( x ) . 1 𝑥 Jacobi-polynomial-P 𝛼 1 𝛽 𝑛 𝑥 1 𝑥 Jacobi-polynomial-P 𝛼 𝛽 1 𝑛 𝑥 2 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle(1-x)P^{(\alpha+1,\beta)}_{n}\left(x\right)+(1+x)P% ^{(\alpha,\beta+1)}_{n}\left(x\right)=2P^{(\alpha,\beta)}_{n}\left(x\right).}}
    0 references
    DLMF id
    DLMF:18.9.E4
    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.m2aadec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
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    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1cdec
    0 references
     
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