DLMF:23.6.E27 (Q7270)

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DLMF:23.6.E27
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    Statements

    Defining formula
    ζ ⁡ ( z | 𝕃 1 ) - ζ ⁡ ( z + 2 ⁢ K ⁡ | 𝕃 1 ) + ζ ⁡ ( 2 ⁢ K ⁡ | 𝕃 1 ) = ns ⁡ ( z , k ) , Weierstrass-zeta-on-lattice 𝑧 subscript 𝕃 1 Weierstrass-zeta-on-lattice 𝑧 2 complete-elliptic-integral-first-kind-K 𝑘 subscript 𝕃 1 Weierstrass-zeta-on-lattice 2 complete-elliptic-integral-first-kind-K 𝑘 subscript 𝕃 1 Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\zeta\left(z|\mathbb{L}_{\mspace{1.0mu }1}\right)-% \zeta\left(z+2K|\mathbb{L}_{\mspace{1.0mu }1}\right)+\zeta\left(2K|\mathbb{L}_% {\mspace{1.0mu }1}\right)=\operatorname{ns}\left(z,k\right),}}
    0 references
    DLMF id
    DLMF:23.6.E27
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    ns ⁡ ( z , k ) Jacobi-elliptic-ns 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m3aadec
    0 references
    DLMF:23.2.E5
    Defining formula
    ζ ⁡ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E5.m2aadec
    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.m1ajdec
    0 references
     
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