DLMF:22.10.E5 (Q7020): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Jacobian elliptic function / rank
 
Normal rank
Property / Symbols used: Jacobian elliptic function / qualifier
 
Defining formula:

cn ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}

\Jacobiellcnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E5.m2aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1ddec
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.m1ddec

Latest revision as of 15:10, 2 January 2020

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DLMF:22.10.E5
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    Statements

    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:22.10.E5
    0 references
    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2addec
    0 references
    cn ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E5.m2aadec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1ddec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1ddec
    0 references