DLMF:29.15.E46 (Q8791)

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DLMF:29.15.E46
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    Statements

    Defining formula
    𝑑𝐸 2 ⁒ n + 1 m ⁑ ( z , k 2 ) = dn ⁑ ( z , k ) ⁒ ( 1 2 ⁒ C 0 + βˆ‘ p = 1 n C 2 ⁒ p ⁒ T 2 ⁒ p ⁑ ( sn ⁑ ( z , k ) ) ) , Lame-polynomial-dE π‘š 2 𝑛 1 𝑧 superscript π‘˜ 2 Jacobi-elliptic-dn 𝑧 π‘˜ 1 2 subscript 𝐢 0 superscript subscript 𝑝 1 𝑛 subscript 𝐢 2 𝑝 Chebyshev-polynomial-first-kind-T 2 𝑝 Jacobi-elliptic-sn 𝑧 π‘˜ {\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),}}
    0 references
    DLMF id
    DLMF:29.15.E46
    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.m2abdec
    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.m2addec
    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.m2acdec
    0 references
    LamΓ© polynomial
    Defining formula
    𝑑𝐸 2 ⁒ n + 1 m ⁑ ( z , k 2 ) Lame-polynomial-dE π‘š 2 𝑛 1 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{dE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z}% ,\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E4.m2aadec
    0 references
    Q12357
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1sdec
    0 references
    Q12367
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C29.S1.XMD2.m1akdec
    0 references
    Q12359
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1aadec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1kdec
    0 references
    Q12350
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1wdec
    0 references
    Q12368
    Defining formula
    C 2 ⁒ p subscript 𝐢 2 𝑝 {\displaystyle{\displaystyle C_{2p}}}
    xml-id
    C29.S6.XMD4.m1dec
    0 references
     
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