DLMF:22.10.E2 (Q7017): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1adec

Latest revision as of 15:09, 2 January 2020

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DLMF:22.10.E2
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    Statements

    Defining formula
    cn ⁡ ( z , k ) = 1 - z 2 2 ! + ( 1 + 4 ⁢ k 2 ) ⁢ z 4 4 ! - ( 1 + 44 ⁢ k 2 + 16 ⁢ k 4 ) ⁢ z 6 6 ! + O ⁡ ( z 8 ) , Jacobi-elliptic-cn 𝑧 𝑘 1 superscript 𝑧 2 2 1 4 superscript 𝑘 2 superscript 𝑧 4 4 1 44 superscript 𝑘 2 16 superscript 𝑘 4 superscript 𝑧 6 6 Big-O superscript 𝑧 8 {\displaystyle{\displaystyle\operatorname{cn}\left(z,k\right)=1-\frac{z^{2}}{2% !}+\left(1+4k^{2}\right)\frac{z^{4}}{4!}-\left(1+44k^{2}+16k^{4}\right)\frac{z% ^{6}}{6!}+O\left(z^{8}\right),}}
    0 references
    DLMF id
    DLMF:22.10.E2
    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
    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.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1adec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1adec
    0 references
     
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