DLMF:18.33.E8 (Q6015): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1fdec

Revision as of 13:27, 2 January 2020

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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
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    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
    0 references
     
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