DLMF:18.33.E10 (Q6017): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11792 / rank
 
Normal rank
Property / Symbols used: Q11792 / qualifier
 
test:

p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}

p_{n}(x)
Property / Symbols used: Q11792 / qualifier
 
xml-id: C18.S33.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11794 / rank
 
Normal rank
Property / Symbols used: Q11794 / qualifier
 
test:

A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}

A_{n}
Property / Symbols used: Q11794 / qualifier
 
xml-id: C18.S33.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11795 / rank
 
Normal rank
Property / Symbols used: Q11795 / qualifier
 
test:

B n subscript 𝐵 𝑛 {\displaystyle{\displaystyle B_{n}}}

B_{n}
Property / Symbols used: Q11795 / qualifier
 
xml-id: C18.S33.XMD5.m1dec

Latest revision as of 12:27, 2 January 2020

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DLMF:18.33.E10
No description defined

    Statements

    test
    z - n ⁢ ϕ 2 ⁢ n ⁢ ( z ) = A n ⁢ p n ⁢ ( 1 2 ⁢ ( z + z - 1 ) ) + B n ⁢ ( z - z - 1 ) ⁢ q n - 1 ⁢ ( 1 2 ⁢ ( z + z - 1 ) ) , superscript 𝑧 𝑛 subscript italic-ϕ 2 𝑛 𝑧 subscript 𝐴 𝑛 subscript 𝑝 𝑛 1 2 𝑧 superscript 𝑧 1 subscript 𝐵 𝑛 𝑧 superscript 𝑧 1 subscript 𝑞 𝑛 1 1 2 𝑧 superscript 𝑧 1 {\displaystyle{\displaystyle z^{-n}\phi_{2n}(z)={A_{n}p_{n}\left(\tfrac{1}{2}(% z+z^{-1})\right)+B_{n}(z-z^{-1})q_{n-1}\left(\tfrac{1}{2}(z+z^{-1})\right)},}}
    0 references
    DLMF id
    DLMF:18.33.E10
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q11750
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1hdec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
    Q11791
    test
    ϕ n ⁢ ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    xml-id
    C18.S33.XMD1.m1hdec
    0 references
    Q11793
    test
    q n ⁢ ( x ) subscript 𝑞 𝑛 𝑥 {\displaystyle{\displaystyle q_{n}(x)}}
    xml-id
    C18.S33.XMD2.m1adec
    0 references
    Q11792
    test
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S33.XMD3.m1adec
    0 references
    Q11794
    test
    A n subscript 𝐴 𝑛 {\displaystyle{\displaystyle A_{n}}}
    xml-id
    C18.S33.XMD4.m1dec
    0 references
    Q11795
    test
    B n subscript 𝐵 𝑛 {\displaystyle{\displaystyle B_{n}}}
    xml-id
    C18.S33.XMD5.m1dec
    0 references
     
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