DLMF:23.22.E3 (Q7390): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aadec
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.m2abdec
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.m2adec
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: Q12049 / rank
 
Normal rank
Property / Symbols used: Q12049 / qualifier
 
test:

ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}

\omega_{1}
Property / Symbols used: Q12049 / qualifier
 
xml-id: C23.S1.XMD8.m1bdec

Latest revision as of 00:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:23.22.E3
No description defined

    Statements

    2 ω 1 = 2 e - π i / 3 ω 3 = ( Γ ( 1 3 ) ) 3 2 π d 1 / 6 . 2 subscript 𝜔 1 2 superscript 𝑒 𝜋 𝑖 3 subscript 𝜔 3 superscript Euler-Gamma 1 3 3 2 𝜋 superscript 𝑑 1 6 {\displaystyle{\displaystyle 2\omega_{1}=2e^{-\pi i/3}\omega_{3}=\frac{\left(% \Gamma\left(\frac{1}{3}\right)\right)^{3}}{2\pi d^{1/6}}.}}
    0 references
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
    0 references
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    C23.S1.XMD8.m1bdec
    0 references