DLMF:3.5.E39 (Q1294): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(7 intermediate revisions by the same user not shown)
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
 
test:

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.m2agdec
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.m1andec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2afdec
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.m2acdec
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.m3andec
Property / Symbols used
 
Property / Symbols used: Q11174 / rank
 
Normal rank
Property / Symbols used: Q11174 / qualifier
 
test:

g ⁢ ( t ) 𝑔 𝑡 {\displaystyle{\displaystyle g(t)}}

g(t)
Property / Symbols used: Q11174 / qualifier
 
xml-id: C3.S5.XMD18.m1adec
Property / Symbols used
 
Property / Symbols used: Laplace transform of $$g(t)$$ (locally) / rank
 
Normal rank
Property / Symbols used: Laplace transform of $$g(t)$$ (locally) / qualifier
 
test:

G ⁢ ( p ) 𝐺 𝑝 {\displaystyle{\displaystyle G(p)}}

G(p)
Property / Symbols used: Laplace transform of $$g(t)$$ (locally) / qualifier
 
xml-id: C3.S5.XMD19.m1adec
Property / Symbols used
 
Property / Symbols used: Q11175 / rank
 
Normal rank
Property / Symbols used: Q11175 / qualifier
 
test:

σ 𝜎 {\displaystyle{\displaystyle\sigma}}

\sigma
Property / Symbols used: Q11175 / qualifier
 
xml-id: C3.S5.XMD20.m1dec

Latest revision as of 16:52, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:3.5.E39
No description defined

    Statements

    test
    g ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ ∫ σ - i ⁢ ∞ σ + i ⁢ ∞ e t ⁢ p ⁢ G ⁢ ( p ) ⁢ d p , 𝑔 𝑡 1 2 imaginary-unit superscript subscript 𝜎 imaginary-unit 𝜎 imaginary-unit superscript 𝑒 𝑡 𝑝 𝐺 𝑝 𝑝 {\displaystyle{\displaystyle g(t)=\frac{1}{2\pi\mathrm{i}}\int_{\sigma-\mathrm% {i}\infty}^{\sigma+\mathrm{i}\infty}e^{tp}G(p)\mathrm{d}p,}}
    0 references
    DLMF id
    DLMF:3.5.E39
    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.m2agdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    Q11174
    test
    g ⁢ ( t ) 𝑔 𝑡 {\displaystyle{\displaystyle g(t)}}
    xml-id
    C3.S5.XMD18.m1adec
    0 references
    Laplace transform of $$g(t)$$ (locally)
    test
    G ⁢ ( p ) 𝐺 𝑝 {\displaystyle{\displaystyle G(p)}}
    xml-id
    C3.S5.XMD19.m1adec
    0 references
    Q11175
    test
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C3.S5.XMD20.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q1294&oldid=6462"