DLMF:17.7.E13 (Q5409): Difference between revisions

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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.m6aldec
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.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11711 / rank
 
Normal rank
Property / Symbols used: Q11711 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11711 / qualifier
 
xml-id: C17.S1.XMD4.m1edec

Latest revision as of 15:03, 2 January 2020

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English
DLMF:17.7.E13
No description defined

    Statements

    Defining formula
    ϕ 3 4 ⁡ ( a , a ⁢ q , b 2 ⁢ q 2 ⁢ n - 2 , q - 2 ⁢ n b , b ⁢ q , a 2 ; q 2 , q 2 ) = a n ⁢ ( - q , b / a ; q ) n ⁢ ( 1 - b ⁢ q n - 1 ) ( - a , b ; q ) n ⁢ ( 1 - b ⁢ q 2 ⁢ n - 1 ) . q-hypergeometric-rphis 4 3 𝑎 𝑎 𝑞 superscript 𝑏 2 superscript 𝑞 2 𝑛 2 superscript 𝑞 2 𝑛 𝑏 𝑏 𝑞 superscript 𝑎 2 superscript 𝑞 2 superscript 𝑞 2 superscript 𝑎 𝑛 q-multiple-Pochhammer 𝑞 𝑏 𝑎 𝑞 𝑛 1 𝑏 superscript 𝑞 𝑛 1 q-multiple-Pochhammer 𝑎 𝑏 𝑞 𝑛 1 𝑏 superscript 𝑞 2 𝑛 1 {\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({a,aq,b^{2}q^{2n-2},q^{-2n}% \atop b,bq,a^{2}};q^{2},q^{2}\right)=\frac{a^{n}\left(-q,b/a;q\right)_{n}(1-bq% ^{n-1})}{\left(-a,b;q\right)_{n}(1-bq^{2n-1})}.}}
    0 references
    DLMF id
    DLMF:17.7.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.m6aldec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1ldec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1edec
    0 references
     
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