DLMF:1.10.E9 (Q334): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: number of zeros / rank
 
Normal rank
Property / Symbols used: number of zeros / qualifier
 
DLMF defining formula:

P 𝑃 {\displaystyle{\displaystyle P}}

P
Property / Symbols used: number of zeros / qualifier
 
xml-id: C1.S10.XMD7.m1dec

Revision as of 09:14, 21 December 2021

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DLMF:1.10.E9
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    Statements

    DLMF defining formula
    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
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1gdec
    0 references
    closed contour
    DLMF defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C1.S10.XMD5.m1adec
    0 references
    number of zeros
    DLMF defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C1.S10.XMD6.m1dec
    0 references
    number of zeros
    DLMF defining formula
    P 𝑃 {\displaystyle{\displaystyle P}}
    xml-id
    C1.S10.XMD7.m1dec
    0 references

    Identifiers

     
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