DLMF:17.7.E1 (Q5397): 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.m6adec

Revision as of 15:01, 2 January 2020

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DLMF:17.7.E1
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    Statements

    Defining formula
    ϕ 2 2 ⁡ ( a , q / a - q , b ; q , - b ) = ( a ⁢ b , b ⁢ q / a ; q 2 ) ∞ ( b ; q ) ∞ , q-hypergeometric-rphis 2 2 𝑎 𝑞 𝑎 𝑞 𝑏 𝑞 𝑏 q-multiple-Pochhammer 𝑎 𝑏 𝑏 𝑞 𝑎 superscript 𝑞 2 q-Pochhammer-symbol 𝑏 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{2}}\left({a,q/a\atop-q,b};q,-b\right)% =\frac{\left(ab,bq/a;q^{2}\right)_{\infty}}{\left(b;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.7.E1
    0 references
    constraint
    | b | < 1 𝑏 1 {\displaystyle{\displaystyle|b|<1}}
    0 references
    Symbols used
    Q11298
    Defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2adec
    0 references
    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.m2adec
    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.m6adec
    0 references
     
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