DLMF:17.9.E18 (Q5444): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11710 / qualifier
 
xml-id: C17.S1.XMD10.m1qdec

Revision as of 15:07, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.9.E18
No description defined

    Statements

    Defining formula
    ( ϕ 3 4 ⁡ ( a , b , a ⁢ b ⁢ z , a ⁢ b / z a ⁢ b ⁢ q 1 2 , - a ⁢ b ⁢ q 1 2 , - a ⁢ b ; q , q ) ) 2 = ϕ 4 5 ⁡ ( a 2 , b 2 , a ⁢ b , a ⁢ b ⁢ z , a ⁢ b / z a ⁢ b ⁢ q 1 2 , - a ⁢ b ⁢ q 1 2 , - a ⁢ b , a 2 ⁢ b 2 ; q , q ) , superscript q-hypergeometric-rphis 4 3 𝑎 𝑏 𝑎 𝑏 𝑧 𝑎 𝑏 𝑧 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 𝑞 𝑞 2 q-hypergeometric-rphis 5 4 superscript 𝑎 2 superscript 𝑏 2 𝑎 𝑏 𝑎 𝑏 𝑧 𝑎 𝑏 𝑧 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑞 1 2 𝑎 𝑏 superscript 𝑎 2 superscript 𝑏 2 𝑞 𝑞 {\displaystyle{\displaystyle\left({{}_{4}\phi_{3}}\left({a,b,abz,ab/z\atop abq% ^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab};q,q\right)\right)^{2}={{}_{5}\phi_{4}}% \left({a^{2},b^{2},ab,abz,ab/z\atop abq^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab,a% ^{2}b^{2}};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.9.E18
    0 references
    Symbols used
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2aqdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1qdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5444&oldid=54534"