DLMF:16.19.E2 (Q5282): 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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11690 / rank
 
Normal rank
Property / Symbols used: Q11690 / qualifier
 
Defining formula:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11690 / qualifier
 
xml-id: C16.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11691 / rank
 
Normal rank
Property / Symbols used: Q11691 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11691 / qualifier
 
xml-id: C16.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11692 / rank
 
Normal rank
Property / Symbols used: Q11692 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11692 / qualifier
 
xml-id: C16.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11693 / rank
 
Normal rank
Property / Symbols used: Q11693 / qualifier
 
Defining formula:

a , a 1 , , a p 𝑎 subscript 𝑎 1 subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}

a,a_{1},\ldots,a_{p}
Property / Symbols used: Q11693 / qualifier
 
xml-id: C16.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11694 / rank
 
Normal rank
Property / Symbols used: Q11694 / qualifier
 
Defining formula:

b , b 1 , , b q 𝑏 subscript 𝑏 1 subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}

b,b_{1},\ldots,b_{q}
Property / Symbols used: Q11694 / qualifier
 
xml-id: C16.S1.XMD5.m1adec

Latest revision as of 14:43, 2 January 2020

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DLMF:16.19.E2
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    Statements

    z μ G p , q m , n ( z ; a 1 , , a p b 1 , , b q ) = G p , q m , n ( z ; a 1 + μ , , a p + μ b 1 + μ , , b q + μ ) , superscript 𝑧 𝜇 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 𝜇 subscript 𝑎 𝑝 𝜇 subscript 𝑏 1 𝜇 subscript 𝑏 𝑞 𝜇 {\displaystyle{\displaystyle z^{\mu}{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}+\mu,\dots,a_{p}+% \mu\atop b_{1}+\mu,\dots,b_{q}+\mu}\right),}}
    0 references
    DLMF:16.19.E2
    0 references
    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)}}
    C16.S17.E1.m2aadec
    0 references
    p 𝑝 {\displaystyle{\displaystyle p}}
    C16.S1.XMD1.m1adec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C16.S1.XMD2.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C16.S1.XMD3.m1adec
    0 references
    a , a 1 , , a p 𝑎 subscript 𝑎 1 subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    C16.S1.XMD4.m1adec
    0 references
    b , b 1 , , b q 𝑏 subscript 𝑏 1 subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    C16.S1.XMD5.m1adec
    0 references