DLMF:5.6.E7 (Q2074): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: hyperbolic secant function / rank
 
Normal rank
Property / Symbols used: hyperbolic secant function / qualifier
 
test:

sech z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}

\sech@@{\NVar{z}}
Property / Symbols used: hyperbolic secant function / qualifier
 
xml-id: C4.S28.E6.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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11281 / rank
 
Normal rank
Property / Symbols used: Q11281 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11281 / qualifier
 
xml-id: C5.S1.XMD5.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11278 / rank
 
Normal rank
Property / Symbols used: Q11278 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11278 / qualifier
 
xml-id: C5.S1.XMD6.m1adec

Latest revision as of 18:32, 1 January 2020

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DLMF:5.6.E7
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    Statements

    | Γ ( x + i y ) | ( sech ( π y ) ) 1 / 2 Γ ( x ) , Euler-Gamma 𝑥 imaginary-unit 𝑦 superscript 𝜋 𝑦 1 2 Euler-Gamma 𝑥 {\displaystyle{\displaystyle|\Gamma\left(x+\mathrm{i}y\right)|\geq(% \operatorname{sech}\left(\pi y\right))^{1/2}\Gamma\left(x\right),}}
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    x 1 2 𝑥 1 2 {\displaystyle{\displaystyle x\geq\tfrac{1}{2}}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2afdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    sech z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    C4.S28.E6.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C5.S1.XMD5.m1fdec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C5.S1.XMD6.m1adec
    0 references