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

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\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
 
test:

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
 
test:

C 𝐶 {\displaystyle{\displaystyle C}}

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

Latest revision as of 15:12, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:1.10.E8
No description defined

    Statements

    test
    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 id
    DLMF:1.10.E8
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10760
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1fdec
    0 references
    Q10835
    test
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S10.XMD5.m1dec
    0 references
     
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