DLMF:17.6.E5 (Q5372): 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.m6abdec

Revision as of 14:57, 2 January 2020

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DLMF:17.6.E5
No description defined

    Statements

    Defining formula
    ϕ 1 2 ⁡ ( a , b a ⁢ q / b ; q , - q / b ) = ( - q ; q ) ∞ ⁢ ( a ⁢ q , a ⁢ q 2 / b 2 ; q 2 ) ∞ ( - q / b , a ⁢ q / b ; q ) ∞ , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑎 𝑞 𝑏 𝑞 𝑞 𝑏 q-Pochhammer-symbol 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑞 𝑎 superscript 𝑞 2 superscript 𝑏 2 superscript 𝑞 2 q-multiple-Pochhammer 𝑞 𝑏 𝑎 𝑞 𝑏 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop aq/b};q,-q/b\right% )=\frac{\left(-q;q\right)_{\infty}\left(aq,\ifrac{aq^{2}}{b^{2}};q^{2}\right)_% {\infty}}{\left(-q/b,aq/b;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.6.E5
    0 references
    constraint
    | b | > | q | 𝑏 𝑞 {\displaystyle{\displaystyle|b|>|q|}}
    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.m2acdec
    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.m2addec
    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.m6abdec
    0 references
     
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