DLMF:19.28.E2 (Q6610): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: beta function / rank
 
Normal rank
Property / Symbols used: beta function / qualifier
 
Defining formula:

B ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

\EulerBeta@{\NVar{a}}{\NVar{b}}
Property / Symbols used: beta function / qualifier
 
xml-id: C5.S12.E1.m2aadec

Revision as of 14:17, 2 January 2020

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DLMF:19.28.E2
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    Statements

    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},}}
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    DLMF:19.28.E2
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    R G ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E3.m2adec
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    B ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    C5.S12.E1.m2aadec
    0 references