DLMF:2.1.E9 (Q693): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / constraint
 

{\displaystyle{\displaystyle\mathbb{C}}}

\mathbb{C}
Property / constraint: {\displaystyle{\displaystyle\mathbb{C}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2addec
Property / Symbols used
 
Property / Symbols used: Q10923 / rank
 
Normal rank
Property / Symbols used: Q10923 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\mathbb{C}}}

\Complexes
Property / Symbols used: Q10923 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r1.m2abdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec

Latest revision as of 16:47, 1 January 2020

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English
DLMF:2.1.E9
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    Statements

    e z = 1 + z + O ( z 2 ) , superscript 𝑒 𝑧 1 𝑧 Big-O superscript 𝑧 2 {\displaystyle{\displaystyle e^{z}=1+z+O\left(z^{2}\right),}}
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    DLMF:2.1.E9
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    {\displaystyle{\displaystyle\mathbb{C}}}
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    z 0 𝑧 0 {\displaystyle{\displaystyle z\to 0}}
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    {\displaystyle{\displaystyle\mathbb{C}}}
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2addec
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    {\displaystyle{\displaystyle\mathbb{C}}}
    introduction.Sx4.p1.t1.r1.m2abdec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
    0 references