DLMF:19.25.E37 (Q6545)

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DLMF:19.25.E37
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    Statements

    Defining formula
    ζ ⁡ ( z ) + z ⁢ ℘ ⁡ ( z ) = 2 ⁢ R G ⁡ ( ℘ ⁡ ( z ) - e 1 ⁡ , ℘ ⁡ ( z ) - e 2 ⁡ , ℘ ⁡ ( z ) - e 3 ⁡ ) . Weierstrass-zeta-on-lattice 𝑧 𝕃 𝑧 Weierstrass-P-on-lattice 𝑧 𝕃 2 Carlson-integral-RG Weierstrass-P-on-lattice 𝑧 𝕃 Weierstrass-e-on-lattice 1 𝕃 Weierstrass-P-on-lattice 𝑧 𝕃 Weierstrass-e-on-lattice 2 𝕃 Weierstrass-P-on-lattice 𝑧 𝕃 Weierstrass-e-on-lattice 3 𝕃 {\displaystyle{\displaystyle\zeta\left(z\right)+z\wp\left(z\right)=2R_{G}\left% (\wp\left(z\right)-e_{1},\wp\left(z\right)-e_{2},\wp\left(z\right)-e_{3}\right% ).}}
    0 references
    DLMF id
    DLMF:19.25.E37
    0 references
    Symbols used
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2acdec
    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.m2abdec
    0 references
    Q11869
    Defining formula
    e j ⁡ Weierstrass-e-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle e_{\NVar{j}}}}
    xml-id
    C23.S3.SS1.m1abdec
    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.m2adec
    0 references
    Q11870
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C19.S25.XMD4.m1bdec
    0 references
     
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