DLMF:10.20.E11 (Q3260): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11451 / rank
 
Normal rank
Property / Symbols used: Q11451 / qualifier
 
Defining formula:

ζ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}

\zeta(z)
Property / Symbols used: Q11451 / qualifier
 
xml-id: C10.S20.XMD1.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11454 / rank
 
Normal rank
Property / Symbols used: Q11454 / qualifier
 
Defining formula:

u k subscript 𝑢 𝑘 {\displaystyle{\displaystyle u_{k}}}

u_{k}
Property / Symbols used: Q11454 / qualifier
 
xml-id: C10.S20.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11453 / rank
 
Normal rank
Property / Symbols used: Q11453 / qualifier
 
Defining formula:

U k ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}}

U_{k}(p)
Property / Symbols used: Q11453 / qualifier
 
xml-id: C10.S41.XMD3.m1adec

Latest revision as of 15:40, 2 January 2020

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DLMF:10.20.E11
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    Statements

    B k ( ζ ) = - ζ - 1 2 j = 0 2 k + 1 ( 3 2 ) j u j ζ - 3 j / 2 U 2 k - j + 1 ( ( 1 - z 2 ) - 1 2 ) , subscript 𝐵 𝑘 𝜁 superscript 𝜁 1 2 superscript subscript 𝑗 0 2 𝑘 1 superscript 3 2 𝑗 subscript 𝑢 𝑗 superscript 𝜁 3 𝑗 2 subscript 𝑈 2 𝑘 𝑗 1 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle B_{k}(\zeta)=-\zeta^{-\frac{1}{2}}\sum_{j=0}^{2k+% 1}(\tfrac{3}{2})^{j}u_{j}\zeta^{-3j/2}U_{2k-j+1}\left((1-z^{2})^{-\frac{1}{2}}% \right),}}
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    DLMF:10.20.E11
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    Warning: Falling back to standard tex;
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C10.S1.XMD3.m1gdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1jdec
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    ζ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    C10.S20.XMD1.m1jdec
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    u k subscript 𝑢 𝑘 {\displaystyle{\displaystyle u_{k}}}
    C10.S20.XMD2.m1dec
    0 references
    U k ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}}
    C10.S41.XMD3.m1adec
    0 references