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Prove $ \sum_{i=0}^{n}(-1)^{i}q^{(i+1)i/2}{n\choose i}_{q}{n+m-i\choose n}_{q}=1 $

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#combinatorics #q-analogs
130
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Search for an algebraic proof of a near q-Vandermonde identity.

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#generating-functions #q-analogs #q-series
35
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How to prove that $e_{q_1}(x)>e_{q_2}(x)$ for $q_1>q_2$?

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#real-analysis #sequences-and-series #q-analogs
165
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Reference request: unusual expansion of product of binomial coefficients

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#combinatorics #reference-request #quantum-groups #q-analogs
82
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How do I construct a bijection to prove the $q$-binomial theorem?

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#combinatorics #binomial-coefficients #combinatorial-proofs #q-analogs
81
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q-Leibniz Rule?

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#calculus #differential-algebra #q-analogs
192
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Alternative q-Analog

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#combinatorics #q-analogs
63
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q-derivative of complex valued functions

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#calculus #combinatorics #complex-analysis #q-analogs
395
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$q$-analog of Number Theory

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#number-theory #soft-question #big-list #q-analogs
75
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Looking for a proper name for this vector subspaces

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#combinatorics #reference-request #terminology #stirling-numbers #q-analogs
79
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Discriminant of numbers

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#number-theory #cyclotomic-polynomials #discriminant #q-analogs
30
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${[n]}_{q,q^{-1}}$ $q$-deformation

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#number-theory #quantum-groups #q-analogs
81
Views

$(p,q)$-Weyl Algebra

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#number-theory #quantum-groups #q-analogs
65
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Proving Gauss’s summation theorem for the $q$-binomial coefficients

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#combinatorics #q-analogs #q-series
47
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$q$-Pochhammer at root of unity

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#combinatorics #number-theory #infinite-product #q-analogs #pochhammer-symbol

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