DLMF:19.28.E2 (Q6610)

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DLMF:19.28.E2
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    Statements

    Defining formula
    ∫ 0 1 t σ - 1 ⁢ R G ⁡ ( 0 , t , 1 ) ⁢ d t = σ 4 ⁢ σ + 2 ⁢ ( B ⁡ ( σ , 1 2 ) ) 2 , superscript subscript 0 1 superscript 𝑡 𝜎 1 Carlson-integral-RG 0 𝑡 1 𝑡 𝜎 4 𝜎 2 superscript Euler-Beta 𝜎 1 2 2 {\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}R_{G}\left(0,t,1\right)% \mathrm{d}t=\frac{\sigma}{4\sigma+2}\left(\mathrm{B}\left(\sigma,\tfrac{1}{2}% \right)\right)^{2},}}
    0 references
    DLMF id
    DLMF:19.28.E2
    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.m2adec
    0 references
     
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