DLMF:22.10.E1 (Q7016): Difference between revisions

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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.m1dec

Revision as of 15:09, 2 January 2020

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DLMF:22.10.E1
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    Statements

    Defining formula
    sn ⁡ ( z , k ) = z - ( 1 + k 2 ) ⁢ z 3 3 ! + ( 1 + 14 ⁢ k 2 + k 4 ) ⁢ z 5 5 ! - ( 1 + 135 ⁢ k 2 + 135 ⁢ k 4 + k 6 ) ⁢ z 7 7 ! + O ⁡ ( z 9 ) , Jacobi-elliptic-sn 𝑧 𝑘 𝑧 1 superscript 𝑘 2 superscript 𝑧 3 3 1 14 superscript 𝑘 2 superscript 𝑘 4 superscript 𝑧 5 5 1 135 superscript 𝑘 2 135 superscript 𝑘 4 superscript 𝑘 6 superscript 𝑧 7 7 Big-O superscript 𝑧 9 {\displaystyle{\displaystyle\operatorname{sn}\left(z,k\right)=z-\left(1+k^{2}% \right)\frac{z^{3}}{3!}+\left(1+14k^{2}+k^{4}\right)\frac{z^{5}}{5!}-\left(1+1% 35k^{2}+135k^{4}+k^{6}\right)\frac{z^{7}}{7!}+O\left(z^{9}\right),}}
    0 references
    DLMF id
    DLMF:22.10.E1
    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.m2adec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11985
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1dec
    0 references
     
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