DLMF:1.10.E9 (Q364): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec
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.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
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.m1gdec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q10836 / rank
 
Normal rank
Property / Symbols used: Q10836 / qualifier
 
test:

N 𝑁 {\displaystyle{\displaystyle N}}

N
Property / Symbols used: Q10836 / qualifier
 
xml-id: C1.S10.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q10837 / rank
 
Normal rank
Property / Symbols used: Q10837 / qualifier
 
test:

P 𝑃 {\displaystyle{\displaystyle P}}

P
Property / Symbols used: Q10837 / qualifier
 
xml-id: C1.S10.XMD7.m1dec

Latest revision as of 15:12, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:1.10.E9
No description defined

    Statements

    test
    N - P = 1 2 ⁢ π ⁢ i ⁢ ∫ C f ′ ⁢ ( z ) f ⁢ ( z ) ⁢ d z = 1 2 ⁢ π ⁢ Δ C ⁢ ( ph ⁡ f ⁢ ( z ) ) , 𝑁 𝑃 1 2 𝜋 𝑖 subscript 𝐶 superscript 𝑓 ′ 𝑧 𝑓 𝑧 𝑧 1 2 𝜋 subscript Δ 𝐶 phase 𝑓 𝑧 {\displaystyle{\displaystyle N-P=\frac{1}{2\pi i}\int_{C}\frac{f^{\prime}(z)}{% f(z)}\mathrm{d}z=\frac{1}{2\pi}\Delta_{C}(\operatorname{ph}f(z)),}}
    0 references
    DLMF id
    DLMF:1.10.E9
    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.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q10760
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1gdec
    0 references
    Q10835
    test
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S10.XMD5.m1adec
    0 references
    Q10836
    test
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C1.S10.XMD6.m1dec
    0 references
    Q10837
    test
    P 𝑃 {\displaystyle{\displaystyle P}}
    xml-id
    C1.S10.XMD7.m1dec
    0 references
     
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