DLMF:5.4.E4 (Q2040): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

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.m2acdec

Revision as of 19:28, 1 January 2020

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DLMF:5.4.E4
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    Γ ( 1 2 + i y ) Γ ( 1 2 - i y ) = | Γ ( 1 2 + i y ) | 2 = π cosh ( π y ) , Euler-Gamma 1 2 imaginary-unit 𝑦 Euler-Gamma 1 2 imaginary-unit 𝑦 superscript Euler-Gamma 1 2 imaginary-unit 𝑦 2 𝜋 𝜋 𝑦 {\displaystyle{\displaystyle\Gamma\left(\tfrac{1}{2}+\mathrm{i}y\right)\Gamma% \left(\tfrac{1}{2}-\mathrm{i}y\right)=\left|\Gamma\left(\tfrac{1}{2}+\mathrm{i% }y\right)\right|^{2}=\frac{\pi}{\cosh\left(\pi y\right)},}}
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    DLMF:5.4.E4
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
    0 references