DLMF:17.9.E14 (Q5440): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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

Revision as of 15:07, 2 January 2020

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DLMF:17.9.E14
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    Statements

    Defining formula
    ϕ 3 4 ⁡ ( q - n , a , b , c d , e , f ; q , q ) = ( e / a , f / a ; q ) n ( e , f ; q ) n ⁢ a n ⁢ ϕ 3 4 ⁡ ( q - n , a , d / b , d / c d , a ⁢ q 1 - n / e , a ⁢ q 1 - n / f ; q , q ) = ( a , e ⁢ f / ( a ⁢ b ) , e ⁢ f / ( a ⁢ c ) ; q ) n ( e , f , e ⁢ f / ( a ⁢ b ⁢ c ) ; q ) n ⁢ ϕ 3 4 ⁡ ( q - n , e / a , f / a , e ⁢ f / ( a ⁢ b ⁢ c ) e ⁢ f / ( a ⁢ b ) , e ⁢ f / ( a ⁢ c ) , q 1 - n / a ; q , q ) . q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑎 𝑏 𝑐 𝑑 𝑒 𝑓 𝑞 𝑞 q-multiple-Pochhammer 𝑒 𝑎 𝑓 𝑎 𝑞 𝑛 q-multiple-Pochhammer 𝑒 𝑓 𝑞 𝑛 superscript 𝑎 𝑛 q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑎 superscript 𝑞 1 𝑛 𝑒 𝑎 superscript 𝑞 1 𝑛 𝑓 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑒 𝑓 𝑎 𝑏 𝑒 𝑓 𝑎 𝑐 𝑞 𝑛 q-multiple-Pochhammer 𝑒 𝑓 𝑒 𝑓 𝑎 𝑏 𝑐 𝑞 𝑛 q-hypergeometric-rphis 4 3 superscript 𝑞 𝑛 𝑒 𝑎 𝑓 𝑎 𝑒 𝑓 𝑎 𝑏 𝑐 𝑒 𝑓 𝑎 𝑏 𝑒 𝑓 𝑎 𝑐 superscript 𝑞 1 𝑛 𝑎 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},a,b,c\atop d,e,f};q,% q\right)=\frac{\left(e/a,f/a;q\right)_{n}}{\left(e,f;q\right)_{n}}a^{n}{{}_{4}% \phi_{3}}\left({q^{-n},a,d/b,d/c\atop d,aq^{1-n}/e,aq^{1-n}/f};q,q\right)=% \frac{\left(a,ef/(ab),ef/(ac);q\right)_{n}}{\left(e,f,ef/(abc);q\right)_{n}}{{% }_{4}\phi_{3}}\left({q^{-n},e/a,f/a,ef/(abc)\atop ef/(ab),ef/(ac),q^{1-n}/a};q% ,q\right).}}
    0 references
    DLMF id
    DLMF:17.9.E14
    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.m2amdec
    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
     
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