DLMF:16.19.E5 (Q5285): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Meijer $$G$$ -function / rank
 
Normal rank
Property / Symbols used: Meijer $$G$$ -function / qualifier
 
Defining formula:

G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle{G^{\NVar{m},\NVar{n}}_{\NVar{p},\NVar{q}}}\left(% \NVar{z};{\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},\dots,b_{q}}}\right)}}

\MeijerG{\NVar{m}}{\NVar{n}}{\NVar{p}}{\NVar{q}}@@{\NVar{z}}{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}
Property / Symbols used: Meijer $$G$$ -function / qualifier
 
xml-id: C16.S17.E1.m2addec

Revision as of 14:44, 2 January 2020

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DLMF:16.19.E5
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    Defining formula
    ϑ ⁢ G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) = G p , q m , n ⁡ ( z ; a 1 - 1 , a 2 , … , a p b 1 , … , b q ) + ( a 1 - 1 ) ⁢ G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) , italic-ϑ Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 1 subscript 𝑎 2 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 subscript 𝑎 1 1 Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle\vartheta{G^{m,n}_{p,q}}\left(z;{a_{1},\dots,a_{p}% \atop b_{1},\dots,b_{q}}\right)={G^{m,n}_{p,q}}\left(z;{a_{1}-1,a_{2},\dots,a_% {p}\atop b_{1},\dots,b_{q}}\right)+(a_{1}-1){G^{m,n}_{p,q}}\left(z;{a_{1},% \dots,a_{p}\atop b_{1},\dots,b_{q}}\right),}}
    0 references
    DLMF id
    DLMF:16.19.E5
    0 references
    Symbols used
    Meijer $$G$$ -function
    Defining formula
    G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle{G^{\NVar{m},\NVar{n}}_{\NVar{p},\NVar{q}}}\left(% \NVar{z};{\NVar{a_{1},\dots,a_{p}}\atop\NVar{b_{1},\dots,b_{q}}}\right)}}
    xml-id
    C16.S17.E1.m2addec
    0 references
     
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