DLMF:23.6.E29 (Q7272)

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DLMF:23.6.E29
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    ζ ( z | 𝕃 3 ) - ζ ( z + 2 i K | 𝕃 3 ) - ζ ( 2 i K | 𝕃 3 ) = cs ( z , k ) . Weierstrass-zeta-on-lattice 𝑧 subscript 𝕃 3 Weierstrass-zeta-on-lattice 𝑧 2 imaginary-unit complementary-complete-elliptic-integral-first-kind-K 𝑘 subscript 𝕃 3 Weierstrass-zeta-on-lattice 2 imaginary-unit complementary-complete-elliptic-integral-first-kind-K 𝑘 subscript 𝕃 3 Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\zeta\left(z|\mathbb{L}_{\mspace{1.0mu }3}\right)-% \zeta\left(z+2\mathrm{i}{K^{\prime}}|\mathbb{L}_{\mspace{1.0mu }3}\right)-% \zeta\left(2\mathrm{i}{K^{\prime}}|\mathbb{L}_{\mspace{1.0mu }3}\right)=% \operatorname{cs}\left(z,k\right).}}
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    DLMF:23.6.E29
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