DLMF:22.10.E6 (Q7021): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1edec

Latest revision as of 15:10, 2 January 2020

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DLMF:22.10.E6
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    Statements

    Defining formula
    dn ⁡ ( z , k ) = 1 - k 2 2 ⁢ sin 2 ⁡ z + O ⁡ ( k 4 ) , Jacobi-elliptic-dn 𝑧 𝑘 1 superscript 𝑘 2 2 2 𝑧 Big-O superscript 𝑘 4 {\displaystyle{\displaystyle\operatorname{dn}\left(z,k\right)=1-\frac{k^{2}}{2% }{\sin^{2}}z+O\left(k^{4}\right),}}
    0 references
    DLMF id
    DLMF:22.10.E6
    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.m2aedec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1edec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1edec
    0 references
     
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