DLMF:29.15.E49 (Q8794)

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DLMF:29.15.E49
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    Statements

    Defining formula
    𝑐𝑑𝐸 2 ⁢ n + 2 m ⁡ ( z , k 2 ) = cn ⁡ ( z , k ) ⁢ dn ⁡ ( z , k ) ⁢ ∑ p = 0 n D 2 ⁢ p + 1 ⁢ U 2 ⁢ p ⁡ ( sn ⁡ ( z , k ) ) , Lame-polynomial-cdE 𝑚 2 𝑛 2 𝑧 superscript 𝑘 2 Jacobi-elliptic-cn 𝑧 𝑘 Jacobi-elliptic-dn 𝑧 𝑘 superscript subscript 𝑝 0 𝑛 subscript 𝐷 2 𝑝 1 Chebyshev-polynomial-second-kind-U 2 𝑝 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{cdE}^{m}_{2n+2}\left(z,k^{2}\right)=% \operatorname{cn}\left(z,k\right)\operatorname{dn}\left(z,k\right)\sum_{p=0}^{% n}D_{2p+1}U_{2p}\left(\operatorname{sn}\left(z,k\right)\right),}}
    0 references
    DLMF id
    DLMF:29.15.E49
    0 references
    Symbols used
    Q11661
    Defining formula
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2abdec
    0 references
     
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