DLMF:1.10.E10 (Q365): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2acdec
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.m1acdec
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.m2acdec
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.m3acdec
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.m1hdec
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.m1bdec

Latest revision as of 16:12, 1 January 2020

No description defined
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English
DLMF:1.10.E10
No description defined

    Statements

    Defining formula
    1 2 ⁢ π ⁢ i ⁢ ∫ C z ⁢ f ′ ⁢ ( z ) f ⁢ ( z ) ⁢ d z = (sum of locations of zeros) - (sum of locations of poles) , 1 2 𝜋 𝑖 subscript 𝐶 𝑧 superscript 𝑓 ′ 𝑧 𝑓 𝑧 𝑧 (sum of locations of zeros) (sum of locations of poles) {\displaystyle{\displaystyle\frac{1}{2\pi i}\int_{C}\frac{zf^{\prime}(z)}{f(z)% }\mathrm{d}z=\mbox{(sum of locations of zeros)}-\mbox{(sum of locations of % poles)},}}
    0 references
    DLMF id
    DLMF:1.10.E10
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1hdec
    0 references
    Q10835
    Defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S10.XMD5.m1bdec
    0 references
     
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