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DLMF:19.25.E38 - MaRDI portal

DLMF:19.25.E38 (Q7242)

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DLMF:19.25.E38
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    Statements

    DLMF defining formula
    ω j = R F ⁡ ( 0 , e j ⁡ - e k ⁡ , e j ⁡ - e ℓ ⁡ ) , subscript 𝜔 𝑗 Carlson-integral-RF 0 Weierstrass-e-on-lattice 𝑗 𝕃 Weierstrass-e-on-lattice 𝑘 𝕃 Weierstrass-e-on-lattice 𝑗 𝕃 Weierstrass-e-on-lattice ℓ 𝕃 {\displaystyle{\displaystyle\omega_{j}=R_{F}\left(0,e_{j}-e_{k},e_{j}-e_{\ell}% \right),}}
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    DLMF 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.m2andec
    0 references
    Q11872
    DLMF defining formula
    e j ⁡ Weierstrass-e-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle e_{\NVar{j}}}}
    xml-id
    C23.S3.SS1.m1acdec
    0 references
    ( = 1 , 2 , 3 )
    DLMF defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C19.S25.XMD3.m1adec
    0 references
    ( = 1 , 2 , 3 )
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S25.XMD5.m1dec
    0 references
    ( = 1 , 2 , 3 )
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C19.S25.XMD6.m1dec
    0 references
    nonzero complex number
    DLMF defining formula
    ω j subscript 𝜔 𝑗 {\displaystyle{\displaystyle\omega_{j}}}
    xml-id
    C19.S25.XMD7.m1dec
    0 references

    Identifiers

     
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