DLMF:5.6.E6 (Q2073): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m2aedec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11281 / rank
 
Normal rank
Property / Symbols used: Q11281 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11281 / qualifier
 
xml-id: C5.S1.XMD5.m1edec
Property / Symbols used
 
Property / Symbols used: Q11278 / rank
 
Normal rank
Property / Symbols used: Q11278 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11278 / qualifier
 
xml-id: C5.S1.XMD6.m1dec

Latest revision as of 19:32, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:5.6.E6
No description defined

    Statements

    | Γ ( x + i y ) | | Γ ( x ) | , Euler-Gamma 𝑥 imaginary-unit 𝑦 Euler-Gamma 𝑥 {\displaystyle{\displaystyle|\Gamma\left(x+\mathrm{i}y\right)|\leq|\Gamma\left% (x\right)|,}}
    0 references
    DLMF:5.6.E6
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aedec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C5.S1.XMD5.m1edec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C5.S1.XMD6.m1dec
    0 references