DLMF:29.6.E38 (Q8668)

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DLMF:29.6.E38
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    Statements

    Defining formula
    𝐸𝑠 Ξ½ 2 ⁒ m + 1 ⁑ ( z , k 2 ) = dn ⁑ ( z , k ) ⁒ βˆ‘ p = 0 ∞ D 2 ⁒ p + 1 ⁒ sin ⁑ ( ( 2 ⁒ p + 1 ) ⁒ Ο• ) , Lame-Es 2 π‘š 1 𝜈 𝑧 superscript π‘˜ 2 Jacobi-elliptic-dn 𝑧 π‘˜ superscript subscript 𝑝 0 subscript 𝐷 2 𝑝 1 2 𝑝 1 italic-Ο• {\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 π‘˜ {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2abdec
    0 references
    Q12364
    Defining formula
    𝐸𝑠 Ξ½ m ⁑ ( z , k 2 ) Lame-Es π‘š 𝜈 𝑧 superscript π‘˜ 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 π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1odec
    0 references
     
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