DLMF:3.5.E35 (Q1290): Difference between revisions

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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.m2adec
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.m3akdec

Latest revision as of 17:51, 1 January 2020

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DLMF:3.5.E35
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    Statements

    Defining formula
    I ⁢ ( f ) = 1 2 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ e ζ ⁢ ζ - s ⁢ f ⁢ ( ζ ) ⁢ d ζ , 𝐼 𝑓 1 2 imaginary-unit superscript subscript 𝑐 imaginary-unit 𝑐 imaginary-unit superscript 𝑒 𝜁 superscript 𝜁 𝑠 𝑓 𝜁 𝜁 {\displaystyle{\displaystyle I(f)=\frac{1}{2\pi\mathrm{i}}\int_{c-\mathrm{i}% \infty}^{c+\mathrm{i}\infty}e^{\zeta}\zeta^{-s}f(\zeta)\mathrm{d}\zeta,}}
    0 references
    DLMF id
    DLMF:3.5.E35
    0 references
    constraint
    c > c 0 > 0 𝑐 subscript 𝑐 0 0 {\displaystyle{\displaystyle c>c_{0}>0}}
    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.m2afdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
     
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