DLMF:1.15.E39 (Q581): 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: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3andec
Property / Symbols used
 
Property / Symbols used: Q10760 / rank
 
Normal rank
Property / Symbols used: Q10760 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q10760 / qualifier
 
xml-id: C1.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q10900 / rank
 
Normal rank
Property / Symbols used: Q10900 / qualifier
 
Defining formula:

Φ ( z ) Φ 𝑧 {\displaystyle{\displaystyle\Phi(z)}}

\Phi(z)
Property / Symbols used: Q10900 / qualifier
 
xml-id: C1.S15.XMD9.m1dec

Latest revision as of 16:32, 1 January 2020

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DLMF:1.15.E39
No description defined

    Statements

    Φ ( z ) = Φ ( x + i y ) = i π - f ( t ) 1 ( x - t ) + i y d t , Φ 𝑧 Φ 𝑥 𝑖 𝑦 𝑖 𝜋 subscript superscript 𝑓 𝑡 1 𝑥 𝑡 𝑖 𝑦 𝑡 {\displaystyle{\displaystyle\Phi(z)=\Phi(x+iy)=\frac{i}{\pi}\int^{\infty}_{-% \infty}f(t)\frac{1}{(x-t)+iy}\mathrm{d}t,}}
    0 references
    DLMF:1.15.E39
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2ahdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1andec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aidec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3andec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C1.S1.XMD1.m1adec
    0 references
    Φ ( z ) Φ 𝑧 {\displaystyle{\displaystyle\Phi(z)}}
    C1.S15.XMD9.m1dec
    0 references