DLMF:23.6.E25 (Q7268)

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DLMF:23.6.E25
No description defined

    Statements

    Defining formula
    ℘ ⁡ ( z + ω 2 ) - e 2 ⁡ = - ( K ⁡ ⁢ k ⁢ k ′ ω 1 ) 2 ⁢ sd 2 ⁡ ( K ⁡ ⁢ z ω 1 , k ) , Weierstrass-P-on-lattice 𝑧 subscript 𝜔 2 𝕃 Weierstrass-e-on-lattice 2 𝕃 superscript complete-elliptic-integral-first-kind-K 𝑘 𝑘 superscript 𝑘 ′ subscript 𝜔 1 2 Jacobi-elliptic-sd 2 complete-elliptic-integral-first-kind-K 𝑘 𝑧 subscript 𝜔 1 𝑘 {\displaystyle{\displaystyle\wp\left(z+\omega_{2}\right)-e_{2}=-\left(\frac{% Kkk^{\prime}}{\omega_{1}}\right)^{2}{\operatorname{sd}^{2}}\left(\frac{K\!z}{% \omega_{1}},k\right),}}
    0 references
    DLMF id
    DLMF:23.6.E25
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sd ⁡ ( z , k ) Jacobi-elliptic-sd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sd}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m2adec
    0 references
    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.m2ahdec
    0 references
    Q11869
    Defining formula
    e j ⁡ Weierstrass-e-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle e_{\NVar{j}}}}
    xml-id
    C23.S3.SS1.m1aodec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1ahdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1vdec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1kdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1wdec
    0 references
    Q12062
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C23.S6.XMD3.m1idec
    0 references
    Q12070
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C23.S6.XMD4.m1edec
    0 references
     
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