DLMF:29.15.E48 (Q8793)

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DLMF:29.15.E48
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    Statements

    Defining formula
    𝑠𝑑𝐸 2 ⁒ n + 2 m ⁑ ( z , k 2 ) = dn ⁑ ( z , k ) ⁒ βˆ‘ p = 0 n C 2 ⁒ p + 1 ⁒ T 2 ⁒ p + 1 ⁑ ( sn ⁑ ( z , k ) ) , Lame-polynomial-sdE π‘š 2 𝑛 2 𝑧 superscript π‘˜ 2 Jacobi-elliptic-dn 𝑧 π‘˜ superscript subscript 𝑝 0 𝑛 subscript 𝐢 2 𝑝 1 Chebyshev-polynomial-first-kind-T 2 𝑝 1 Jacobi-elliptic-sn 𝑧 π‘˜ {\displaystyle{\displaystyle\mathit{sdE}^{m}_{2n+2}\left(z,k^{2}\right)=% \operatorname{dn}\left(z,k\right)\sum_{p=0}^{n}C_{2p+1}T_{2p+1}\left(% \operatorname{sn}\left(z,k\right)\right),}}
    0 references
    DLMF id
    DLMF:29.15.E48
    0 references
    Symbols used
    Q11207
    Defining formula
    T n ⁑ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 π‘₯ {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2acdec
    0 references
    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.m2aedec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁑ ( z , k ) Jacobi-elliptic-sn 𝑧 π‘˜ {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2aedec
    0 references
    LamΓ© polynomial
    Defining formula
    𝑠𝑑𝐸 2 ⁒ n + 2 m ⁑ ( z , k 2 ) Lame-polynomial-sdE π‘š 2 𝑛 2 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{sdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z% },\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E6.m2aadec
    0 references
    Q12357
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1udec
    0 references
     
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