DLMF:17.9.E13 (Q5439): Difference between revisions

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‎Changed an Item: Add constraint
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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

Revision as of 15:07, 2 January 2020

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DLMF:17.9.E13
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    Statements

    Defining formula
    ϕ 2 3 ⁡ ( a , b , c d , e ; q , d ⁢ e a ⁢ b ⁢ c ) = ( e / b , e / c ; q ) ∞ ( e , e / ( b ⁢ c ) ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( d / a , b , c d , b ⁢ c ⁢ q / e ; q , q ) + ( d / a , b , c , d ⁢ e / ( b ⁢ c ) ; q ) ∞ ( d , e , b ⁢ c / e , d ⁢ e / ( a ⁢ b ⁢ c ) ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( e / b , e / c , d ⁢ e / ( a ⁢ b ⁢ c ) d ⁢ e / ( b ⁢ c ) , e ⁢ q / ( b ⁢ c ) ; q , q ) . q-hypergeometric-rphis 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 𝑞 𝑑 𝑒 𝑎 𝑏 𝑐 q-multiple-Pochhammer 𝑒 𝑏 𝑒 𝑐 𝑞 q-multiple-Pochhammer 𝑒 𝑒 𝑏 𝑐 𝑞 q-hypergeometric-rphis 3 2 𝑑 𝑎 𝑏 𝑐 𝑑 𝑏 𝑐 𝑞 𝑒 𝑞 𝑞 q-multiple-Pochhammer 𝑑 𝑎 𝑏 𝑐 𝑑 𝑒 𝑏 𝑐 𝑞 q-multiple-Pochhammer 𝑑 𝑒 𝑏 𝑐 𝑒 𝑑 𝑒 𝑎 𝑏 𝑐 𝑞 q-hypergeometric-rphis 3 2 𝑒 𝑏 𝑒 𝑐 𝑑 𝑒 𝑎 𝑏 𝑐 𝑑 𝑒 𝑏 𝑐 𝑒 𝑞 𝑏 𝑐 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop d,e};q,\frac{de}% {abc}\right)=\frac{\left(e/b,e/c;q\right)_{\infty}}{\left(e,e/(bc);q\right)_{% \infty}}{{}_{3}\phi_{2}}\left({d/a,b,c\atop d,bcq/e};q,q\right)+\frac{\left(d/% a,b,c,de/(bc);q\right)_{\infty}}{\left(d,e,bc/e,de/(abc);q\right)_{\infty}}{{}% _{3}\phi_{2}}\left({e/b,e/c,de/(abc)\atop de/(bc),eq/(bc)};q,q\right).}}
    0 references
    DLMF id
    DLMF:17.9.E13
    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.m2aldec
    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
     
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