DLMF:2.5.E14 (Q790): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.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.m2acdec
Property / Symbols used
 
Property / Symbols used: order less than / rank
 
Normal rank
Property / Symbols used: order less than / qualifier
 
test:

o ( x ) little-o 𝑥 {\displaystyle{\displaystyle o\left(\NVar{x}\right)}}

\littleo@{\NVar{x}}
Property / Symbols used: order less than / qualifier
 
xml-id: C2.S1.E2.m2adec

Latest revision as of 16:03, 1 January 2020

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DLMF:2.5.E14
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    Statements

    | Γ ( x + i y ) | = 2 π e - π | y | / 2 | y | x - ( 1 / 2 ) ( 1 + o ( 1 ) ) , Euler-Gamma 𝑥 𝑖 𝑦 2 𝜋 superscript 𝑒 𝜋 𝑦 2 superscript 𝑦 𝑥 1 2 1 little-o 1 {\displaystyle{\displaystyle|\Gamma\left(x+iy\right)|=\sqrt{2\pi}e^{-\pi|y|/2}% |y|^{x-(1/2)}\left(1+o\left(1\right)\right),}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2abdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aedec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2acdec
    0 references
    o ( x ) little-o 𝑥 {\displaystyle{\displaystyle o\left(\NVar{x}\right)}}
    C2.S1.E2.m2adec
    0 references