DLMF:18.33.E11 (Q6018): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11797 / rank
 
Normal rank
Property / Symbols used: Q11797 / qualifier
 
Defining formula:

D n subscript 𝐷 𝑛 {\displaystyle{\displaystyle D_{n}}}

D_{n}
Property / Symbols used: Q11797 / qualifier
 
xml-id: C18.S33.XMD7.m1dec

Latest revision as of 13:28, 2 January 2020

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DLMF:18.33.E11
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    Statements

    Defining formula
    z - n + 1 ⁢ ϕ 2 ⁢ n - 1 ⁢ ( z ) = C n ⁢ p n ⁢ ( 1 2 ⁢ ( z + z - 1 ) ) + D n ⁢ ( z - z - 1 ) ⁢ q n - 1 ⁢ ( 1 2 ⁢ ( z + z - 1 ) ) , superscript 𝑧 𝑛 1 subscript italic-ϕ 2 𝑛 1 𝑧 subscript 𝐶 𝑛 subscript 𝑝 𝑛 1 2 𝑧 superscript 𝑧 1 subscript 𝐷 𝑛 𝑧 superscript 𝑧 1 subscript 𝑞 𝑛 1 1 2 𝑧 superscript 𝑧 1 {\displaystyle{\displaystyle z^{-n+1}\phi_{2n-1}(z)={C_{n}p_{n}\left(\tfrac{1}% {2}(z+z^{-1})\right)+D_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)% },}}
    0 references
    DLMF id
    DLMF:18.33.E11
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1idec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1idec
    0 references
    Q11791
    Defining formula
    ϕ n ⁢ ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    xml-id
    C18.S33.XMD1.m1idec
    0 references
    Q11793
    Defining formula
    q n ⁢ ( x ) subscript 𝑞 𝑛 𝑥 {\displaystyle{\displaystyle q_{n}(x)}}
    xml-id
    C18.S33.XMD2.m1bdec
    0 references
    Q11792
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S33.XMD3.m1bdec
    0 references
    Q11796
    Defining formula
    C n subscript 𝐶 𝑛 {\displaystyle{\displaystyle C_{n}}}
    xml-id
    C18.S33.XMD6.m1dec
    0 references
    Q11797
    Defining formula
    D n subscript 𝐷 𝑛 {\displaystyle{\displaystyle D_{n}}}
    xml-id
    C18.S33.XMD7.m1dec
    0 references
     
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