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DLMF:32.8.E6 - MaRDI portal

DLMF:32.8.E6 (Q10046)

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DLMF:32.8.E6
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    Statements

    DLMF defining formula
    Q n + 1 ⁢ ( z ) ⁢ Q n - 1 ⁢ ( z ) = z ⁢ Q n 2 ⁢ ( z ) + 4 ⁢ ( Q n ′ ⁢ ( z ) ) 2 - 4 ⁢ Q n ⁢ ( z ) ⁢ Q n ′′ ⁢ ( z ) , subscript 𝑄 𝑛 1 𝑧 subscript 𝑄 𝑛 1 𝑧 𝑧 superscript subscript 𝑄 𝑛 2 𝑧 4 superscript superscript subscript 𝑄 𝑛 ′ 𝑧 2 4 subscript 𝑄 𝑛 𝑧 superscript subscript 𝑄 𝑛 ′′ 𝑧 {\displaystyle{\displaystyle Q_{n+1}(z)Q_{n-1}(z)={zQ_{n}^{2}(z)+4\left(Q_{n}^% {\prime}(z)\right)^{2}-4Q_{n}(z)Q_{n}^{\prime\prime}(z)},}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C32.S1.XMD2.m1adec
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    real
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1edec
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    polynomial
    DLMF defining formula
    Q n ⁢ ( z ) subscript 𝑄 𝑛 𝑧 {\displaystyle{\displaystyle Q_{n}(z)}}
    xml-id
    C32.S8.XMD1.m1adec
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