DLMF:19.18.E4 (Q6347): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: multivariate hypergeometric function / rank
 
Normal rank
Property / Symbols used: multivariate hypergeometric function / qualifier
 
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)}}

\Carlsonmultivarhyper{\NVar{-a}}@{\NVar{b_{1}},\dots,\NVar{b_{n}}}{\NVar{z_{1}},\dots,\NVar{z_{n}}}
Property / Symbols used: multivariate hypergeometric function / qualifier
 
xml-id: C19.S16.E9.m2adec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11853 / rank
 
Normal rank
Property / Symbols used: Q11853 / qualifier
 
Defining formula:

w j subscript 𝑤 𝑗 {\displaystyle{\displaystyle w_{j}}}

w_{j}
Property / Symbols used: Q11853 / qualifier
 
xml-id: C19.S18.XMD1.m1adec

Latest revision as of 13:54, 2 January 2020

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DLMF:19.18.E4
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    Statements

    Defining formula
    ∂ j ⁡ R - a ⁡ ( 𝐛 ; 𝐳 ) = - a ⁢ w j ⁢ R - a - 1 ⁡ ( 𝐛 + 𝐞 j ; 𝐳 ) , subscript 𝑗 Carlson-integral-R 𝑎 𝐛 𝐳 𝑎 subscript 𝑤 𝑗 Carlson-integral-R 𝑎 1 𝐛 subscript 𝐞 𝑗 𝐳 {\displaystyle{\displaystyle\partial_{j}R_{-a}\left(\mathbf{b};\mathbf{z}% \right)=-aw_{j}R_{-a-1}\left(\mathbf{b}+\mathbf{e}_{j};\mathbf{z}\right),}}
    0 references
    DLMF id
    DLMF:19.18.E4
    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.m2adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q11853
    Defining formula
    w j subscript 𝑤 𝑗 {\displaystyle{\displaystyle w_{j}}}
    xml-id
    C19.S18.XMD1.m1adec
    0 references
     
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