DLMF:22.10.E5 (Q7020)

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DLMF:22.10.E5
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    Statements

    Defining formula
    cn ⁡ ( z , k ) = cos ⁡ z + k 2 4 ⁢ ( z - sin ⁡ z ⁢ cos ⁡ z ) ⁢ sin ⁡ z + O ⁡ ( k 4 ) , Jacobi-elliptic-cn 𝑧 𝑘 𝑧 superscript 𝑘 2 4 𝑧 𝑧 𝑧 𝑧 Big-O superscript 𝑘 4 {\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=\cos z+\frac{k^{% 2}}{4}(z-\sin z\cos z)\sin z+O\left(k^{4}\right),}}
    0 references
    DLMF id
    DLMF:22.10.E5
    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.m2addec
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    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2aadec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1ddec
    0 references
     
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