DLMF:19.16.E19 (Q6337): 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.m2abdec

Revision as of 13:53, 2 January 2020

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DLMF:19.16.E19
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    Statements

    Defining formula
    R - a ⁡ ( b 1 , … , b n ; 0 , z 2 , … , z n ) = B ⁡ ( a , a ′ - b 1 ) B ⁡ ( a , a ′ ) ⁢ R - a ⁡ ( b 2 , … , b n ; z 2 , … , z n ) , Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 0 subscript 𝑧 2 … subscript 𝑧 𝑛 Euler-Beta 𝑎 superscript 𝑎 ′ subscript 𝑏 1 Euler-Beta 𝑎 superscript 𝑎 ′ Carlson-integral-R 𝑎 subscript 𝑏 2 … subscript 𝑏 𝑛 subscript 𝑧 2 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{-a}\left(b_{1},\dots,b_{n};0,z_{2},\dots,z_{n}% \right)=\frac{\mathrm{B}\left(a,a^{\prime}-b_{1}\right)}{\mathrm{B}\left(a,a^{% \prime}\right)}R_{-a}\left(b_{2},\dots,b_{n};z_{2},\dots,z_{n}\right),}}
    0 references
    DLMF id
    DLMF:19.16.E19
    0 references
    constraint
    a ′ > b 1 superscript 𝑎 ′ subscript 𝑏 1 {\displaystyle{\displaystyle a^{\prime}>b_{1}}}
    0 references
    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2aidec
    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.m2abdec
    0 references
     
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