DLMF:17.8.E6 (Q5425): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11713 / rank
 
Normal rank
Property / Symbols used: Q11713 / qualifier
 
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}}}}

\qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11713 / qualifier
 
xml-id: C17.S2.SS1.p1.m6aedec
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

Latest revision as of 15:05, 2 January 2020

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DLMF:17.8.E6
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    Statements

    Defining formula
    ψ 4 4 ⁡ ( - q ⁢ a 1 2 , b , c , d - a 1 2 , a ⁢ q / b , a ⁢ q / c , a ⁢ q / d ; q , q ⁢ a 3 2 b ⁢ c ⁢ d ) = ( a ⁢ q , a ⁢ q / ( b ⁢ c ) , a ⁢ q / ( b ⁢ d ) , a ⁢ q / ( c ⁢ d ) , q ⁢ a 1 2 / b , q ⁢ a 1 2 / c , q ⁢ a 1 2 / d , q , q / a ; q ) ∞ ( a ⁢ q / b , a ⁢ q / c , a ⁢ q / d , q / b , q / c , q / d , q ⁢ a 1 2 , q ⁢ a - 1 2 , q ⁢ a 3 2 / ( b ⁢ c ⁢ d ) ; q ) ∞ , q-hypergeometric-rpsis 4 4 𝑞 superscript 𝑎 1 2 𝑏 𝑐 𝑑 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑞 𝑞 superscript 𝑎 3 2 𝑏 𝑐 𝑑 q-multiple-Pochhammer 𝑎 𝑞 𝑎 𝑞 𝑏 𝑐 𝑎 𝑞 𝑏 𝑑 𝑎 𝑞 𝑐 𝑑 𝑞 superscript 𝑎 1 2 𝑏 𝑞 superscript 𝑎 1 2 𝑐 𝑞 superscript 𝑎 1 2 𝑑 𝑞 𝑞 𝑎 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑎 𝑞 𝑑 𝑞 𝑏 𝑞 𝑐 𝑞 𝑑 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 3 2 𝑏 𝑐 𝑑 𝑞 {\displaystyle{\displaystyle{{}_{4}\psi_{4}}\left({-qa^{\frac{1}{2}},b,c,d% \atop-a^{\frac{1}{2}},aq/b,aq/c,aq/d};q,\frac{qa^{\frac{3}{2}}}{bcd}\right)=% \frac{\left(aq,aq/(bc),aq/(bd),aq/(cd),qa^{\frac{1}{2}}/b,qa^{\frac{1}{2}}/c,% qa^{\frac{1}{2}}/d,q,q/a;q\right)_{\infty}}{\left(aq/b,aq/c,aq/d,q/b,q/c,q/d,% qa^{\frac{1}{2}},qa^{-\frac{1}{2}},qa^{\frac{3}{2}}/(bcd);q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.8.E6
    0 references
    Symbols used
    bilateral basic hypergeometric (or bilateral $$q$$ -hypergeometric) function
    Defining formula
    ψ s r ⁡ ( a 1 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rpsis 𝑟 𝑠 subscript 𝑎 1 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r}}\psi_{\NVar{s}}}\left(\NVar{a_{1},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E3.m2acdec
    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
     
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