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

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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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English
DLMF:5.6.E7
No description defined

    Statements

    test
    | 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),}}
    0 references
    DLMF id
    DLMF:5.6.E7
    0 references
    constraint
    x ≥ 1 2 𝑥 1 2 {\displaystyle{\displaystyle x\geq\tfrac{1}{2}}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    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
    hyperbolic secant function
    test
    sech ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}
    xml-id
    C4.S28.E6.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q11281
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C5.S1.XMD5.m1fdec
    0 references
    Q11278
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C5.S1.XMD6.m1adec
    0 references
     
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