DLMF:10.24.E3 (Q3479): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
imported>Admin
 
(2 intermediate revisions by the same user not shown)
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11477 / rank
 
Normal rank
Property / Symbols used: Q11477 / qualifier
 
test:

γ ν subscript 𝛾 𝜈 {\displaystyle{\displaystyle\gamma_{\nu}}}

\gamma_{\nu}
Property / Symbols used: Q11477 / qualifier
 
xml-id: C10.S24.XMD1.m1dec

Latest revision as of 13:33, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.24.E3
No description defined

    Statements

    Γ ( 1 + i ν ) = ( π ν sinh ( π ν ) ) 1 2 e i γ ν , Euler-Gamma 1 𝑖 𝜈 superscript 𝜋 𝜈 𝜋 𝜈 1 2 superscript 𝑒 𝑖 subscript 𝛾 𝜈 {\displaystyle{\displaystyle\Gamma\left(1+i\nu\right)=\left(\frac{\pi\nu}{% \sinh\left(\pi\nu\right)}\right)^{\frac{1}{2}}e^{i\gamma_{\nu}},}}
    0 references
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1bdec
    0 references
    γ ν subscript 𝛾 𝜈 {\displaystyle{\displaystyle\gamma_{\nu}}}
    C10.S24.XMD1.m1dec
    0 references