DLMF:10.20.E12 (Q3261): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: coefficients (locally) / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11451 / rank
 
Normal rank
Property / Symbols used: Q11451 / qualifier
 
test:

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

\zeta(z)
Property / Symbols used: Q11451 / qualifier
 
xml-id: C10.S20.XMD1.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11452 / rank
 
Normal rank
Property / Symbols used: Q11452 / qualifier
 
test:

v k subscript 𝑣 𝑘 {\displaystyle{\displaystyle v_{k}}}

v_{k}
Property / Symbols used: Q11452 / qualifier
 
xml-id: C10.S20.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11455 / rank
 
Normal rank
Property / Symbols used: Q11455 / qualifier
 
test:

V k ⁢ ( p ) subscript 𝑉 𝑘 𝑝 {\displaystyle{\displaystyle V_{k}(p)}}

V_{k}(p)
Property / Symbols used: Q11455 / qualifier
 
xml-id: C10.S41.XMD4.m1dec

Latest revision as of 14:40, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.20.E12
No description defined

    Statements

    test
    C k ⁢ ( ζ ) = - ζ 1 2 ⁢ ∑ j = 0 2 ⁢ k + 1 ( 3 2 ) j ⁢ v j ⁢ ζ - 3 ⁢ j / 2 ⁢ V 2 ⁢ k - j + 1 ⁢ ( ( 1 - z 2 ) - 1 2 ) , subscript 𝐶 𝑘 𝜁 superscript 𝜁 1 2 superscript subscript 𝑗 0 2 𝑘 1 superscript 3 2 𝑗 subscript 𝑣 𝑗 superscript 𝜁 3 𝑗 2 subscript 𝑉 2 𝑘 𝑗 1 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle C_{k}(\zeta)=-\zeta^{\frac{1}{2}}\sum_{j=0}^{2k+1% }(\tfrac{3}{2})^{j}v_{j}\zeta^{-3j/2}V_{2k-j+1}\left((1-z^{2})^{-\frac{1}{2}}% \right),}}
    0 references
    DLMF id
    DLMF:10.20.E12
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q11428
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1hdec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1kdec
    0 references
    Q11451
    test
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C10.S20.XMD1.m1kdec
    0 references
    Q11452
    test
    v k subscript 𝑣 𝑘 {\displaystyle{\displaystyle v_{k}}}
    xml-id
    C10.S20.XMD3.m1adec
    0 references
    Q11455
    test
    V k ⁢ ( p ) subscript 𝑉 𝑘 𝑝 {\displaystyle{\displaystyle V_{k}(p)}}
    xml-id
    C10.S41.XMD4.m1dec
    0 references
     
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