DLMF:17.7.E6 (Q5402): 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.m1edec

Revision as of 15:02, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.7.E6
No description defined

    Statements

    Defining formula
    ϕ 2 3 ⁡ ( q - 2 ⁢ n , b , c q 1 - 2 ⁢ n / b , q 1 - 2 ⁢ n / c ; q , q 2 - n b ⁢ c ) = ( b , c ; q ) n ⁢ ( q , b ⁢ c ; q ) 2 ⁢ n ( q , b ⁢ c ; q ) n ⁢ ( b , c ; q ) 2 ⁢ n . q-hypergeometric-rphis 3 2 superscript 𝑞 2 𝑛 𝑏 𝑐 superscript 𝑞 1 2 𝑛 𝑏 superscript 𝑞 1 2 𝑛 𝑐 𝑞 superscript 𝑞 2 𝑛 𝑏 𝑐 q-multiple-Pochhammer 𝑏 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑏 𝑐 𝑞 2 𝑛 q-multiple-Pochhammer 𝑞 𝑏 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑏 𝑐 𝑞 2 𝑛 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({q^{-2n},b,c\atop q^{1-2n}/b% ,q^{1-2n}/c};q,\frac{q^{2-n}}{bc}\right)=\frac{\left(b,c;q\right)_{n}\left(q,% bc;q\right)_{2n}}{\left(q,bc;q\right)_{n}\left(b,c;q\right)_{2n}}.}}
    0 references
    DLMF id
    DLMF:17.7.E6
    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.m2aedec
    0 references
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6aedec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1edec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5402&oldid=53538"