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

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(6 intermediate revisions by the same user not shown)
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.m2acdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
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.m1cdec
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
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.m1cdec
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.m1cdec
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.m1cdec

Latest revision as of 14:44, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:16.19.E4
No description defined

    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
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1cdec
    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.m1cdec
    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.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5284&oldid=50310"