DLMF:17.7.E20 (Q5416): Difference between revisions

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imported>Admin
 
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Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
test:

( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11715 / rank
 
Normal rank
Property / Symbols used: Q11715 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11715 / qualifier
 
xml-id: C17.S1.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11710 / qualifier
 
xml-id: C17.S1.XMD10.m1sdec
Property / Symbols used
 
Property / Symbols used: Q11711 / rank
 
Normal rank
Property / Symbols used: Q11711 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11711 / qualifier
 
xml-id: C17.S1.XMD4.m1hdec

Latest revision as of 14:04, 2 January 2020

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Language Label Description Also known as
English
DLMF:17.7.E20
No description defined

    Statements

    test
    ∑ k = 0 n 1 - a ⁢ p k ⁢ q k 1 - a ⁢ ( a ; p ) k ⁢ ( c ; q ) k ( q ; q ) k ⁢ ( a ⁢ p / c ; p ) k ⁢ c - k = ( a ⁢ p ; p ) n ⁢ ( c ⁢ q ; q ) n ( q ; q ) n ⁢ ( a ⁢ p / c ; p ) n ⁢ c - n . superscript subscript 𝑘 0 𝑛 1 𝑎 superscript 𝑝 𝑘 superscript 𝑞 𝑘 1 𝑎 q-Pochhammer-symbol 𝑎 𝑝 𝑘 q-Pochhammer-symbol 𝑐 𝑞 𝑘 q-Pochhammer-symbol 𝑞 𝑞 𝑘 q-Pochhammer-symbol 𝑎 𝑝 𝑐 𝑝 𝑘 superscript 𝑐 𝑘 q-Pochhammer-symbol 𝑎 𝑝 𝑝 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑎 𝑝 𝑐 𝑝 𝑛 superscript 𝑐 𝑛 {\displaystyle{\displaystyle\sum_{k=0}^{n}\frac{1-ap^{k}q^{k}}{1-a}\frac{\left% (a;p\right)_{k}\left(c;q\right)_{k}}{\left(q;q\right)_{k}\left(ap/c;p\right)_{% k}}c^{-k}=\frac{\left(ap;p\right)_{n}\left(cq;q\right)_{n}}{\left(q;q\right)_{% n}\left(ap/c;p\right)_{n}}c^{-n}.}}
    0 references
    DLMF id
    DLMF:17.7.E20
    0 references
    Symbols used
    Q11298
    test
    ( 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
    Q11715
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C17.S1.XMD1.m1dec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1sdec
    0 references
    Q11711
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1hdec
    0 references
     
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