DLMF:17.2.E11 (Q5301): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
Defining formula:

( 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.m2ajdec
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.m1jdec
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.m1gdec

Latest revision as of 14:46, 2 January 2020

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DLMF:17.2.E11
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    Statements

    ( a q - n ; q ) n = ( q / a ; q ) n ( - a q ) n q - ( n 2 ) , q-Pochhammer-symbol 𝑎 superscript 𝑞 𝑛 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑎 𝑞 𝑛 superscript 𝑎 𝑞 𝑛 superscript 𝑞 binomial 𝑛 2 {\displaystyle{\displaystyle\left(aq^{-n};q\right)_{n}=\left(q/a;q\right)_{n}% \left(-\frac{a}{q}\right)^{n}q^{-\genfrac{(}{)}{0.0pt}{}{n}{2}},}}
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    DLMF:17.2.E11
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    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1acdec
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    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    C17.S2.SS1.p1.m2ajdec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1jdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C17.S1.XMD4.m1gdec
    0 references