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DLMF:18.22.E10 - MaRDI portal

DLMF:18.22.E10 (Q6574)

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DLMF:18.22.E10
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    Statements

    DLMF defining formula
    A ⁢ ( x ) ⁢ p n ⁢ ( x + 1 ) - ( A ⁢ ( x ) + C ⁢ ( x ) ) ⁢ p n ⁢ ( x ) + C ⁢ ( x ) ⁢ p n ⁢ ( x - 1 ) - n ⁢ ( n + α + β + 1 ) ⁢ p n ⁢ ( x ) = 0 , 𝐴 𝑥 subscript 𝑝 𝑛 𝑥 1 𝐴 𝑥 𝐶 𝑥 subscript 𝑝 𝑛 𝑥 𝐶 𝑥 subscript 𝑝 𝑛 𝑥 1 𝑛 𝑛 𝛼 𝛽 1 subscript 𝑝 𝑛 𝑥 0 {\displaystyle{\displaystyle A(x)p_{n}(x+1)-\left(A(x)+C(x)\right)p_{n}(x)+C(x% )p_{n}(x-1)-n(n+\alpha+\beta+1)p_{n}(x)=0,}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1jdec
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    polynomial of degree n
    DLMF defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1fdec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1hdec
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    coefficient
    DLMF defining formula
    A ⁢ ( x ) 𝐴 𝑥 {\displaystyle{\displaystyle A(x)}}
    xml-id
    C18.S22.XMD7.m1dec
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    coefficient
    DLMF defining formula
    C ⁢ ( x ) 𝐶 𝑥 {\displaystyle{\displaystyle C(x)}}
    xml-id
    C18.S22.XMD8.m1dec
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    Identifiers

     
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