DLMF:19.25.E40 (Q6548)

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DLMF:19.25.E40
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    Statements

    Defining formula
    z = σ ⁡ ( z ) ⁢ R F ⁡ ( σ 1 2 ⁢ ( z ) , σ 2 2 ⁢ ( z ) , σ 3 2 ⁢ ( z ) ) , 𝑧 Weierstrass-sigma-on-lattice 𝑧 𝕃 Carlson-integral-RF superscript subscript 𝜎 1 2 𝑧 superscript subscript 𝜎 2 2 𝑧 superscript subscript 𝜎 3 2 𝑧 {\displaystyle{\displaystyle z=\sigma\left(z\right)R_{F}\left(\sigma_{1}^{2}(z% ),\sigma_{2}^{2}(z),\sigma_{3}^{2}(z)\right),}}
    0 references
    DLMF id
    DLMF:19.25.E40
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2aodec
    0 references
    DLMF:23.2.E6
    Defining formula
    σ ⁡ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E6.m2adec
    0 references
     
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