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

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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

Revision as of 13:33, 2 January 2020

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DLMF:10.24.E3
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    Statements

    test
    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
    DLMF id
    DLMF:10.24.E3
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    hyperbolic sine function
    test
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
     
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