DLMF:17.8.E1 (Q5420): Difference between revisions

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imported>Admin
 
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Property / Symbols used
 
Property / Symbols used: Q11713 / rank
 
Normal rank
Property / Symbols used: Q11713 / qualifier
 
test:

( 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
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.m1dec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11718 / rank
 
Normal rank
Property / Symbols used: Q11718 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11718 / qualifier
 
xml-id: C17.S1.XMD7.m1dec

Latest revision as of 14:04, 2 January 2020

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DLMF:17.8.E1
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    Statements

    n = - ( - z ) n q n ( n - 1 ) / 2 = ( q , z , q / z ; q ) ; superscript subscript 𝑛 superscript 𝑧 𝑛 superscript 𝑞 𝑛 𝑛 1 2 q-multiple-Pochhammer 𝑞 𝑧 𝑞 𝑧 𝑞 {\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2}=% \left(q,z,q/z;q\right)_{\infty};}}
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    ( 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}}}}
    C17.S2.SS1.p1.m6adec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C17.S1.XMD4.m1dec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C17.S1.XMD7.m1dec
    0 references