DLMF:19.28.E1 (Q6609)

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DLMF:19.28.E1
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    Statements

    Defining formula
    ∫ 0 1 t σ - 1 ⁢ R F ⁡ ( 0 , t , 1 ) ⁢ d t = 1 2 ⁢ ( B ⁡ ( σ , 1 2 ) ) 2 , superscript subscript 0 1 superscript 𝑡 𝜎 1 Carlson-integral-RF 0 𝑡 1 𝑡 1 2 superscript Euler-Beta 𝜎 1 2 2 {\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}R_{F}\left(0,t,1\right)% \mathrm{d}t=\tfrac{1}{2}\left(\mathrm{B}\left(\sigma,\tfrac{1}{2}\right)\right% )^{2},}}
    0 references
    DLMF id
    DLMF:19.28.E1
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    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.m2adec
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    beta function
    Defining formula
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2adec
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