DLMF:23.6.E28 (Q7271)

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DLMF:23.6.E28
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    Statements

    Defining formula
    ΞΆ ⁑ ( z | 𝕃 2 ) - ΞΆ ⁑ ( z + 2 ⁒ K ⁑ | 𝕃 2 ) + ΞΆ ⁑ ( 2 ⁒ K ⁑ | 𝕃 2 ) = ds ⁑ ( z , k ) , Weierstrass-zeta-on-lattice 𝑧 subscript 𝕃 2 Weierstrass-zeta-on-lattice 𝑧 2 complete-elliptic-integral-first-kind-K π‘˜ subscript 𝕃 2 Weierstrass-zeta-on-lattice 2 complete-elliptic-integral-first-kind-K π‘˜ subscript 𝕃 2 Jacobi-elliptic-ds 𝑧 π‘˜ {\displaystyle{\displaystyle\zeta\left(z|\mathbb{L}_{\mspace{1.0mu }2}\right)-% \zeta\left(z+2K|\mathbb{L}_{\mspace{1.0mu }2}\right)+\zeta\left(2K|\mathbb{L}_% {\mspace{1.0mu }2}\right)=\operatorname{ds}\left(z,k\right),}}
    0 references
    DLMF id
    DLMF:23.6.E28
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    ds ⁑ ( z , k ) Jacobi-elliptic-ds 𝑧 π‘˜ {\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E7.m3aadec
    0 references
    DLMF:23.2.E5
    Defining formula
    ΞΆ ⁑ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E5.m2abdec
    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.m1akdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1ydec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1ndec
    0 references
    Q12062
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C23.S6.XMD3.m1ldec
    0 references
     
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