DLMF:22.15.E11 (Q7106): Difference between revisions

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

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

\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
Property / Symbols used: Jacobian elliptic function / qualifier
 
xml-id: C22.S2.E4.m2aadec

Revision as of 15:28, 2 January 2020

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DLMF:22.15.E11
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    Statements

    Defining formula
    x = ∫ 0 sn ⁡ ( x , k ) d t ( 1 - t 2 ) ⁢ ( 1 - k 2 ⁢ t 2 ) , 𝑥 superscript subscript 0 Jacobi-elliptic-sn 𝑥 𝑘 𝑡 1 superscript 𝑡 2 1 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle x=\int_{0}^{\operatorname{sn}\left(x,k\right)}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E11
    0 references
    constraint
    0 ≤ k ≤ 1 0 𝑘 1 {\displaystyle{\displaystyle 0\leq k\leq 1}}
    0 references
    Symbols used
    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.m2aadec
    0 references
     
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