DLMF:19.28.E1 (Q6609): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec

Revision as of 14:17, 2 January 2020

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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
    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.m2adec
    0 references
    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
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
     
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