DLMF:17.2.E27 (Q5317): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: $$q$$ -binomial coefficient (or Gaussian polynomial) / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
test:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1ahdec
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.m2azdec
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.m1zdec
Property / Symbols used
 
Property / Symbols used: Q11716 / rank
 
Normal rank
Property / Symbols used: Q11716 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11716 / qualifier
 
xml-id: C17.S1.XMD3.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.m1wdec

Latest revision as of 13:48, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.2.E27
No description defined

    Statements

    test
    [ n m ] q = ( q ; q ) n ( q ; q ) m ⁢ ( q ; q ) n - m = ( q - n ; q ) m ⁢ ( - 1 ) m ⁢ q n ⁢ m - ( m 2 ) ( q ; q ) m , q-binomial 𝑛 𝑚 𝑞 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑚 q-Pochhammer-symbol 𝑞 𝑞 𝑛 𝑚 q-Pochhammer-symbol superscript 𝑞 𝑛 𝑞 𝑚 superscript 1 𝑚 superscript 𝑞 𝑛 𝑚 binomial 𝑚 2 q-Pochhammer-symbol 𝑞 𝑞 𝑚 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{n}{m}_{q}=\frac{\left(q;q% \right)_{n}}{\left(q;q\right)_{m}\left(q;q\right)_{n-m}}\\ =\frac{\left(q^{-n};q\right)_{m}(-1)^{m}q^{nm-\genfrac{(}{)}{0.0pt}{}{m}{2}}}{% \left(q;q\right)_{m}},}}
    0 references
    DLMF id
    DLMF:17.2.E27
    0 references
    Symbols used
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1ahdec
    0 references
    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.m2azdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1zdec
    0 references
    Q11716
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C17.S1.XMD3.m1dec
    0 references
    Q11711
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1wdec
    0 references
     
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