DLMF:29.15.E44 (Q8789)

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DLMF:29.15.E44
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    Statements

    Defining formula
    𝑠𝐸 2 ⁒ n + 1 m ⁑ ( z , k 2 ) = βˆ‘ p = 0 n A 2 ⁒ p + 1 ⁒ T 2 ⁒ p + 1 ⁑ ( sn ⁑ ( z , k ) ) , Lame-polynomial-sE π‘š 2 𝑛 1 𝑧 superscript π‘˜ 2 superscript subscript 𝑝 0 𝑛 subscript 𝐴 2 𝑝 1 Chebyshev-polynomial-first-kind-T 2 𝑝 1 Jacobi-elliptic-sn 𝑧 π‘˜ {\displaystyle{\displaystyle\mathit{sE}^{m}_{2n+1}\left(z,k^{2}\right)=\sum_{p% =0}^{n}A_{2p+1}T_{2p+1}\left(\operatorname{sn}\left(z,k\right)\right),}}
    0 references
    DLMF id
    DLMF:29.15.E44
    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.m2aadec
    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.m2aadec
    0 references
    LamΓ© polynomial
    Defining formula
    𝑠𝐸 2 ⁒ n + 1 m ⁑ ( z , k 2 ) Lame-polynomial-sE π‘š 2 𝑛 1 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{sE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z}% ,\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E2.m2aadec
    0 references
    Q12357
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1qdec
    0 references
    Q12367
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C29.S1.XMD2.m1aidec
    0 references
    Q12359
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1ydec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1idec
    0 references
     
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