DLMF:23.10.E11 (Q7309)

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DLMF:23.10.E11
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    Statements

    Defining formula
    n 2 ⁢ ℘ ⁡ ( n ⁢ z ) = ∑ j = 0 n - 1 ∑ ℓ = 0 n - 1 ℘ ⁡ ( z + 2 ⁢ j n ⁢ ω 1 + 2 ⁢ ℓ n ⁢ ω 3 ) , superscript 𝑛 2 Weierstrass-P-on-lattice 𝑛 𝑧 𝕃 superscript subscript 𝑗 0 𝑛 1 superscript subscript ℓ 0 𝑛 1 Weierstrass-P-on-lattice 𝑧 2 𝑗 𝑛 subscript 𝜔 1 2 ℓ 𝑛 subscript 𝜔 3 𝕃 {\displaystyle{\displaystyle n^{2}\wp\left(nz\right)=\sum_{j=0}^{n-1}\sum_{% \ell=0}^{n-1}\wp\left(z+\frac{2j}{n}\omega_{1}+\frac{2\ell}{n}\omega_{3}\right% ),}}
    0 references
    DLMF id
    DLMF:23.10.E11
    0 references
    Symbols used
    DLMF:23.2.E4
    Defining formula
    ℘ ⁡ ( z ) Weierstrass-P-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E4.m2afdec
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    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1jdec
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