DLMF:17.7.E7 (Q5403): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / rank
 
Normal rank
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
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)}}

\qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
xml-id: C17.S4.E1.m2afdec
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.m6afdec
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.m1fdec

Latest revision as of 15:02, 2 January 2020

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English
DLMF:17.7.E7
No description defined

    Statements

    Defining formula
    ϕ 3 4 ⁡ ( a , - q ⁢ a 1 2 , b , c - a 1 2 , a ⁢ q / b , a ⁢ q / c ; q , q ⁢ a 1 2 b ⁢ c ) = ( a ⁢ q , q ⁢ a 1 2 / b , q ⁢ a 1 2 / c , a ⁢ q / ( b ⁢ c ) ; q ) ∞ ( a ⁢ q / b , a ⁢ q / c , q ⁢ a 1 2 , q ⁢ a 1 2 / ( b ⁢ c ) ; q ) ∞ . q-hypergeometric-rphis 4 3 𝑎 𝑞 superscript 𝑎 1 2 𝑏 𝑐 superscript 𝑎 1 2 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 𝑞 superscript 𝑎 1 2 𝑏 𝑐 q-multiple-Pochhammer 𝑎 𝑞 𝑞 superscript 𝑎 1 2 𝑏 𝑞 superscript 𝑎 1 2 𝑐 𝑎 𝑞 𝑏 𝑐 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑏 𝑎 𝑞 𝑐 𝑞 superscript 𝑎 1 2 𝑞 superscript 𝑎 1 2 𝑏 𝑐 𝑞 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({a,-qa^{\frac{1}{2}},b,c% \atop-a^{\frac{1}{2}},aq/b,aq/c};q,\frac{qa^{\frac{1}{2}}}{bc}\right)=\frac{% \left(aq,qa^{\frac{1}{2}}/b,qa^{\frac{1}{2}}/c,aq/(bc);q\right)_{\infty}}{% \left(aq/b,aq/c,qa^{\frac{1}{2}},qa^{\frac{1}{2}}/(bc);q\right)_{\infty}}.}}
    0 references
    DLMF id
    DLMF:17.7.E7
    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.m2afdec
    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.m6afdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1fdec
    0 references
     
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