DLMF:29.6.E38 (Q8668): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1sdec

Revision as of 15:52, 2 January 2020

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DLMF:29.6.E38
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    Statements

    Defining formula
    𝐸𝑠 ν 2 ⁢ m + 1 ⁡ ( z , k 2 ) = dn ⁡ ( z , k ) ⁢ ∑ p = 0 ∞ D 2 ⁢ p + 1 ⁢ sin ⁡ ( ( 2 ⁢ p + 1 ) ⁢ ϕ ) , Lame-Es 2 𝑚 1 𝜈 𝑧 superscript 𝑘 2 Jacobi-elliptic-dn 𝑧 𝑘 superscript subscript 𝑝 0 subscript 𝐷 2 𝑝 1 2 𝑝 1 italic-ϕ {\displaystyle{\displaystyle\mathit{Es}^{2m+1}_{\nu}\left(z,k^{2}\right)=% \operatorname{dn}\left(z,k\right)\sum_{p=0}^{\infty}D_{2p+1}\sin\left((2p+1)% \phi\right),}}
    0 references
    DLMF id
    DLMF:29.6.E38
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2abdec
    0 references
    Q12364
    Defining formula
    𝐸𝑠 ν m ⁡ ( z , k 2 ) Lame-Es 𝑚 𝜈 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    xml-id
    C29.S3.SS4.p1.m6aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q12357
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1odec
    0 references
    Q12359
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1acdec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1edec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1sdec
    0 references
     
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