DLMF:17.5.E5 (Q5367): Difference between revisions

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‎Changed an Item: Add constraint
 
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.m1ddec

Latest revision as of 14:57, 2 January 2020

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DLMF:17.5.E5
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    Statements

    Defining formula
    ϕ 1 1 ⁡ ( a c ; q , c / a ) = ( c / a ; q ) ∞ ( c ; q ) ∞ , q-hypergeometric-rphis 1 1 𝑎 𝑐 𝑞 𝑐 𝑎 q-Pochhammer-symbol 𝑐 𝑎 𝑞 q-Pochhammer-symbol 𝑐 𝑞 {\displaystyle{\displaystyle{{}_{1}\phi_{1}}\left({a\atop c};q,c/a\right)=% \frac{\left(c/a;q\right)_{\infty}}{\left(c;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.5.E5
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    constraint
    | c | < | a | 𝑐 𝑎 {\displaystyle{\displaystyle|c|<|a|}}
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    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.m2addec
    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
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ddec
    0 references
     
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