DLMF:22.16.E7 (Q7126): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec

Revision as of 15:31, 2 January 2020

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DLMF:22.16.E7
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    Statements

    Defining formula
    am ⁡ ( x , k ) = x - 1 4 ⁢ k 2 ⁢ ( x - sin ⁡ x ⁢ cos ⁡ x ) + O ⁡ ( k 4 ) , Jacobi-elliptic-amplitude 𝑥 𝑘 𝑥 1 4 superscript 𝑘 2 𝑥 𝑥 𝑥 Big-O superscript 𝑘 4 {\displaystyle{\displaystyle\operatorname{am}\left(x,k\right)=x-\tfrac{1}{4}k^% {2}(x-\sin x\cos x)+O\left(k^{4}\right),}}
    0 references
    DLMF id
    DLMF:22.16.E7
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    Jacobi’s amplitude function
    Defining formula
    am ⁡ ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S16.E1.m2afdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
     
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