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

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Property / Symbols used
 
Property / Symbols used: Q11701 / rank
 
Normal rank
Property / Symbols used: Q11701 / qualifier
 
Defining formula:

ϑ italic-ϑ {\displaystyle{\displaystyle\vartheta}}

\vartheta
Property / Symbols used: Q11701 / qualifier
 
xml-id: C16.S8.XMD3.m1dec

Latest revision as of 14:44, 2 January 2020

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DLMF:16.19.E5
No description defined

    Statements

    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
    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1ddec
    0 references
    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1ddec
    0 references
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1ddec
    0 references
    Q11693
    Defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1ddec
    0 references
    Q11694
    Defining formula
    b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    xml-id
    C16.S1.XMD5.m1ddec
    0 references
    Q11701
    Defining formula
    ϑ italic-ϑ {\displaystyle{\displaystyle\vartheta}}
    xml-id
    C16.S8.XMD3.m1dec
    0 references
     
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