DLMF:1.10.E8 (Q363): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec
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.m3aadec
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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q10835 / rank
 
Normal rank
Property / Symbols used: Q10835 / qualifier
 
Defining formula:

C 𝐶 {\displaystyle{\displaystyle C}}

C
Property / Symbols used: Q10835 / qualifier
 
xml-id: C1.S10.XMD5.m1dec

Latest revision as of 16:12, 1 January 2020

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DLMF:1.10.E8
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    Statements

    1 2 π i C f ( z ) d z = sum of the residues of  f ( z )  within  C . 1 2 𝜋 𝑖 subscript 𝐶 𝑓 𝑧 𝑧 sum of the residues of  f ( z )  within  C {\displaystyle{\displaystyle\frac{1}{2\pi i}\int_{C}f(z)\mathrm{d}z=\mbox{sum % of the residues of $f(z)$ within $C$}.}}
    0 references
    DLMF:1.10.E8
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C1.S1.XMD1.m1fdec
    0 references
    C 𝐶 {\displaystyle{\displaystyle C}}
    C1.S10.XMD5.m1dec
    0 references