DLMF:29.15.E45 (Q8790): 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.m2abdec

Revision as of 01:36, 2 January 2020

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DLMF:29.15.E45
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    Statements

    Defining formula
    𝑐𝐸 2 ⁢ n + 1 m ⁡ ( z , k 2 ) = cn ⁡ ( z , k ) ⁢ ∑ p = 0 n B 2 ⁢ p + 1 ⁢ U 2 ⁢ p ⁡ ( sn ⁡ ( z , k ) ) , Lame-polynomial-cE 𝑚 2 𝑛 1 𝑧 superscript 𝑘 2 Jacobi-elliptic-cn 𝑧 𝑘 superscript subscript 𝑝 0 𝑛 subscript 𝐵 2 𝑝 1 Chebyshev-polynomial-second-kind-U 2 𝑝 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{cE}^{m}_{2n+1}\left(z,k^{2}\right)=% \operatorname{cn}\left(z,k\right)\sum_{p=0}^{n}B_{2p+1}U_{2p}\left(% \operatorname{sn}\left(z,k\right)\right),}}
    0 references
    DLMF id
    DLMF:29.15.E45
    0 references
    Symbols used
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2adec
    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
    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.m2abdec
    0 references
     
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