DLMF:29.15.E48 (Q9485): Difference between revisions

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DLMF:29.15.E48
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    Statements

    DLMF defining formula
    𝑠𝑑𝐸 2 ⁢ n + 2 m ⁡ ( z , k 2 ) = dn ⁡ ( z , k ) ⁢ ∑ p = 0 n C 2 ⁢ p + 1 ⁢ T 2 ⁢ p + 1 ⁡ ( sn ⁡ ( z , k ) ) , Lame-polynomial-sdE 𝑚 2 𝑛 2 𝑧 superscript 𝑘 2 Jacobi-elliptic-dn 𝑧 𝑘 superscript subscript 𝑝 0 𝑛 subscript 𝐶 2 𝑝 1 Chebyshev-polynomial-first-kind-T 2 𝑝 1 Jacobi-elliptic-sn 𝑧 𝑘 {\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
    Symbols used
    Chebyshev polynomial of the first kind
    DLMF defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2acdec
    0 references
    Jacobian elliptic function
    DLMF 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.m2aedec
    0 references
    Jacobian elliptic function
    DLMF 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.m2aedec
    0 references
    Lamé polynomial
    DLMF defining formula
    𝑠𝑑𝐸 2 ⁢ n + 2 m ⁡ ( z , k 2 ) Lame-polynomial-sdE 𝑚 2 𝑛 2 𝑧 superscript 𝑘 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
    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1udec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C29.S1.XMD2.m1amdec
    0 references
    nonnegative integer
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1mdec
    0 references
    real parameter
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1ydec
    0 references
    coefficents
    DLMF defining formula
    C 2 ⁢ p + 1 subscript 𝐶 2 𝑝 1 {\displaystyle{\displaystyle C_{2p+1}}}
    xml-id
    C29.S6.XMD7.m1hdec
    0 references

    Identifiers

     
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