DLMF:1.9.E33 (Q308): 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.m1aedec
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.m2abdec
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.m2amdec
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.m3aedec
Property / Symbols used
 
Property / Symbols used: Q10813 / rank
 
Normal rank
Property / Symbols used: Q10813 / qualifier
 
test:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q10813 / qualifier
 
xml-id: C1.S9.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q10822 / rank
 
Normal rank
Property / Symbols used: Q10822 / qualifier
 
test:

u ⁢ ( z ) 𝑢 𝑧 {\displaystyle{\displaystyle u(z)}}

u(z)
Property / Symbols used: Q10822 / qualifier
 
xml-id: C1.S9.XMD14.m1dec

Latest revision as of 15:08, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:1.9.E33
No description defined

    Statements

    test
    u ⁢ ( z ) = 1 2 ⁢ π ⁢ ∫ 0 2 ⁢ π u ⁢ ( z + r ⁢ e i ⁢ ϕ ) ⁢ d ϕ . 𝑢 𝑧 1 2 𝜋 subscript superscript 2 𝜋 0 𝑢 𝑧 𝑟 superscript 𝑒 𝑖 italic-ϕ italic-ϕ {\displaystyle{\displaystyle u(z)=\frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})% \mathrm{d}\phi.}}
    0 references
    DLMF id
    DLMF:1.9.E33
    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.m2afdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2amdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q10813
    test
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C1.S9.XMD1.m1edec
    0 references
    Q10822
    test
    u ⁢ ( z ) 𝑢 𝑧 {\displaystyle{\displaystyle u(z)}}
    xml-id
    C1.S9.XMD14.m1dec
    0 references
     
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