DLMF:17.2.E39 (Q5329): Difference between revisions

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

[ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}

\qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}}
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier
 
xml-id: C17.S2.E27.m2ajdec
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.m1akdec
Property / Symbols used
 
Property / Symbols used: Q11712 / rank
 
Normal rank
Property / Symbols used: Q11712 / qualifier
 
test:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q11712 / qualifier
 
xml-id: C17.S1.XMD2.m1gdec
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.m1aidec

Latest revision as of 13:51, 2 January 2020

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DLMF:17.2.E39
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    Statements

    j = 0 n [ n j ] q 2 q j = ( - q ; q ) n , superscript subscript 𝑗 0 𝑛 q-binomial 𝑛 𝑗 superscript 𝑞 2 superscript 𝑞 𝑗 q-Pochhammer-symbol 𝑞 𝑞 𝑛 {\displaystyle{\displaystyle\sum_{j=0}^{n}\genfrac{[}{]}{0.0pt}{}{n}{j}_{q^{2}% }q^{j}=\left(-q;q\right)_{n},}}
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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.m2aagdec
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    [ n m ] q q-binomial 𝑛 𝑚 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{n}}{\NVar{m}}_{\NVar% {q}}}}
    C17.S2.E27.m2ajdec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1akdec
    0 references
    j 𝑗 {\displaystyle{\displaystyle j}}
    C17.S1.XMD2.m1gdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C17.S1.XMD4.m1aidec
    0 references