DLMF:29.14.E8 (Q8742)

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DLMF:29.14.E8
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    Statements

    Defining formula
    𝑠𝑑𝐸 2 ⁒ n + 2 m ⁑ ( s , k 2 ) ⁒ 𝑠𝑑𝐸 2 ⁒ n + 2 m ⁑ ( K ⁑ + i ⁒ t , k 2 ) , Lame-polynomial-sdE π‘š 2 𝑛 2 𝑠 superscript π‘˜ 2 Lame-polynomial-sdE π‘š 2 𝑛 2 complete-elliptic-integral-first-kind-K π‘˜ imaginary-unit 𝑑 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{sdE}^{m}_{2n+2}\left(s,k^{2}\right)\mathit% {sdE}^{m}_{2n+2}\left(K+\mathrm{i}t,k^{2}\right),}}
    0 references
    DLMF id
    DLMF:29.14.E8
    0 references
    Symbols used
    LamΓ© polynomial
    Defining formula
    𝑠𝑑𝐸 2 ⁒ n + 2 m ⁑ ( z , k 2 ) Lame-polynomial-sdE π‘š 2 𝑛 2 𝑧 superscript π‘˜ 2 {\displaystyle{\displaystyle\mathit{sdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z% },\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E6.m2adec
    0 references
    Q11600
    Defining formula
    K ⁑ ( k ) complete-elliptic-integral-first-kind-K π‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1agdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    Q12357
    Defining formula
    m π‘š {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1edec
    0 references
    Q12367
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C29.S1.XMD2.m1edec
    0 references
    Q12350
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1gdec
    0 references
     
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