DLMF:31.10.E12 (Q9063): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12498 / rank
 
Normal rank
Property / Symbols used: Q12498 / qualifier
 
Defining formula:

C 1 subscript 𝐶 1 {\displaystyle{\displaystyle C_{1}}}

C_{1}
Property / Symbols used: Q12498 / qualifier
 
xml-id: C31.S10.XMD11.m1dec
Property / Symbols used
 
Property / Symbols used: weight function (locally) / rank
 
Normal rank
Property / Symbols used: weight function (locally) / qualifier
 
Defining formula:

ρ ( s , t ) 𝜌 𝑠 𝑡 {\displaystyle{\displaystyle\rho(s,t)}}

\rho(s,t)
Property / Symbols used: weight function (locally) / qualifier
 
xml-id: C31.S10.XMD12.m1dec
Property / Symbols used
 
Property / Symbols used: kernel (locally) / rank
 
Normal rank
Property / Symbols used: kernel (locally) / qualifier
 
Defining formula:

𝒦 ( z ; s , t ) 𝒦 𝑧 𝑠 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}

\mathcal{K}(z;s,t)
Property / Symbols used: kernel (locally) / qualifier
 
xml-id: C31.S10.XMD13.m1dec
Property / Symbols used
 
Property / Symbols used: Q12499 / rank
 
Normal rank
Property / Symbols used: Q12499 / qualifier
 
Defining formula:

w 𝑤 {\displaystyle{\displaystyle w}}

w
Property / Symbols used: Q12499 / qualifier
 
xml-id: C31.S10.XMD16.m1dec

Latest revision as of 13:37, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:31.10.E12
No description defined

    Statements

    W ( z ) = C 1 C 2 𝒦 ( z ; s , t ) w ( s ) w ( t ) ρ ( s , t ) d s d t 𝑊 𝑧 subscript subscript 𝐶 1 subscript subscript 𝐶 2 𝒦 𝑧 𝑠 𝑡 𝑤 𝑠 𝑤 𝑡 𝜌 𝑠 𝑡 𝑠 𝑡 {\displaystyle{\displaystyle W(z)=\int_{C_{1}}\int_{C_{2}}\mathcal{K}(z;s,t)w(% s)w(t)\rho(s,t)\mathrm{d}s\mathrm{d}t}}
    0 references
    DLMF:31.10.E12
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C31.S1.XMD1.m1fdec
    0 references
    C 1 subscript 𝐶 1 {\displaystyle{\displaystyle C_{1}}}
    C31.S10.XMD11.m1dec
    0 references
    ρ ( s , t ) 𝜌 𝑠 𝑡 {\displaystyle{\displaystyle\rho(s,t)}}
    C31.S10.XMD12.m1dec
    0 references
    𝒦 ( z ; s , t ) 𝒦 𝑧 𝑠 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
    C31.S10.XMD13.m1dec
    0 references
    w 𝑤 {\displaystyle{\displaystyle w}}
    C31.S10.XMD16.m1dec
    0 references