DLMF:29.15.E46 (Q8791)

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DLMF:29.15.E46
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    𝑑𝐸 2 n + 1 m ( z , k 2 ) = dn ( z , k ) ( 1 2 C 0 + p = 1 n C 2 p T 2 p ( sn ( z , k ) ) ) , Lame-polynomial-dE 𝑚 2 𝑛 1 𝑧 superscript 𝑘 2 Jacobi-elliptic-dn 𝑧 𝑘 1 2 subscript 𝐶 0 superscript subscript 𝑝 1 𝑛 subscript 𝐶 2 𝑝 Chebyshev-polynomial-first-kind-T 2 𝑝 Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\mathit{dE}^{m}_{2n+1}\left(z,k^{2}\right)=% \operatorname{dn}\left(z,k\right)\left(\tfrac{1}{2}C_{0}+\sum_{p=1}^{n}C_{2p}T% _{2p}\left(\operatorname{sn}\left(z,k\right)\right)\right),}}
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    DLMF:29.15.E46
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    T n ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r4.m2abdec
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    dn ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m2addec
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