DLMF:18.33.E8 (Q6015)

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DLMF:18.33.E8
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    Statements

    Defining formula
    p n ⁢ ( 1 2 ⁢ ( z + z - 1 ) ) = (const.) × ( z - n ⁢ ϕ 2 ⁢ n ⁢ ( z ) + z n ⁢ ϕ 2 ⁢ n ⁢ ( z - 1 ) ) = (const.) × ( z - n + 1 ⁢ ϕ 2 ⁢ n - 1 ⁢ ( z ) + z n - 1 ⁢ ϕ 2 ⁢ n - 1 ⁢ ( z - 1 ) ) , subscript 𝑝 𝑛 1 2 𝑧 superscript 𝑧 1 (const.) superscript 𝑧 𝑛 subscript italic-ϕ 2 𝑛 𝑧 superscript 𝑧 𝑛 subscript italic-ϕ 2 𝑛 superscript 𝑧 1 (const.) superscript 𝑧 𝑛 1 subscript italic-ϕ 2 𝑛 1 𝑧 superscript 𝑧 𝑛 1 subscript italic-ϕ 2 𝑛 1 superscript 𝑧 1 {\displaystyle{\displaystyle p_{n}\left(\tfrac{1}{2}(z+z^{-1})\right)=\text{(% const.)}\times{\left(z^{-n}\phi_{2n}(z)+z^{n}\phi_{2n}(z^{-1})\right)}=\text{(% const.)}\times{\left(z^{-n+1}\phi_{2n-1}(z)+z^{n-1}\phi_{2n-1}(z^{-1})\right)}% ,}}
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    DLMF id
    DLMF:18.33.E8
    0 references
    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1fdec
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    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
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    Q11791
    Defining formula
    ϕ n ⁢ ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    xml-id
    C18.S33.XMD1.m1fdec
    0 references
    Q11792
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S33.XMD3.m1dec
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