DLMF:16.19.E4 (Q5284): Difference between revisions

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‎Changed an Item: Add constraint
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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.m1cdec

Revision as of 14:44, 2 January 2020

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DLMF:16.19.E4
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    Statements

    Defining formula
    G p , q m , n ⁡ ( z ; a 1 , … , a p b 1 , … , b q ) = 2 p + 1 + b 1 + … + b q - m - n - a 1 - … - a p π m + n - 1 2 ⁢ ( p + q ) ⁢ G 2 ⁢ p , 2 ⁢ q 2 ⁢ m , 2 ⁢ n ⁡ ( 2 2 ⁢ p - 2 ⁢ q ⁢ z 2 ; 1 2 ⁢ a 1 , 1 2 ⁢ a 1 + 1 2 , … , 1 2 ⁢ a p , 1 2 ⁢ a p + 1 2 1 2 ⁢ b 1 , 1 2 ⁢ b 1 + 1 2 , … , 1 2 ⁢ b q , 1 2 ⁢ b q + 1 2 ) , Meijer-G 𝑚 𝑛 𝑝 𝑞 𝑧 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 superscript 2 𝑝 1 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑚 𝑛 subscript 𝑎 1 … subscript 𝑎 𝑝 superscript 𝜋 𝑚 𝑛 1 2 𝑝 𝑞 Meijer-G 2 𝑚 2 𝑛 2 𝑝 2 𝑞 superscript 2 2 𝑝 2 𝑞 superscript 𝑧 2 1 2 subscript 𝑎 1 1 2 subscript 𝑎 1 1 2 … 1 2 subscript 𝑎 𝑝 1 2 subscript 𝑎 𝑝 1 2 1 2 subscript 𝑏 1 1 2 subscript 𝑏 1 1 2 … 1 2 subscript 𝑏 𝑞 1 2 subscript 𝑏 𝑞 1 2 {\displaystyle{\displaystyle{G^{m,n}_{p,q}}\left(z;{a_{1},\dots,a_{p}\atop b_{% 1},\dots,b_{q}}\right)=\frac{2^{p+1+b_{1}+\dots+b_{q}-m-n-a_{1}-\dots-a_{p}}}{% \pi^{m+n-\frac{1}{2}(p+q)}}{G^{2m,2n}_{2p,2q}}\left(2^{2p-2q}z^{2};{\frac{1}{2% }a_{1},\frac{1}{2}a_{1}+\frac{1}{2},\dots,\frac{1}{2}a_{p},\frac{1}{2}a_{p}+% \frac{1}{2}\atop\frac{1}{2}b_{1},\frac{1}{2}b_{1}+\frac{1}{2},\dots,\frac{1}{2% }b_{q},\frac{1}{2}b_{q}+\frac{1}{2}}\right),}}
    0 references
    DLMF id
    DLMF:16.19.E4
    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1cdec
    0 references
    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1cdec
    0 references
     
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