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$q$-derivative satisfying linear approximation characterization

Published on
#derivatives #asymptotics #q-analogs
34
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What is meant by "q-generalisation"?

Published on
#continued-fractions #q-analogs
405
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Good article or book to q-analogs?

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#calculus #combinatorics #reference-request #q-analogs
121
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Formula for $q$-Analogue of Eulerian Polynomial

Published on
#combinatorics #algebraic-combinatorics #q-analogs #eulerian-numbers
376
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Barnes' double gamma function versus q-gamma function

Published on
#special-functions #q-analogs
313
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The groupoid cardinality of $\mathbb{F}_q$-vector spaces $\sum_{n=0}^{\infty} \, \bigl(\prod_{i=0}^{n-1} q^n-q^i\bigr)^{-1}$

Published on
#sequences-and-series #category-theory #closed-form #q-analogs
104
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How to prove that $\sum_{i=0}^n\frac{(a;q)_i}{(q;q)_i}\frac{(b;q)_{n-i}}{(q;q)_{n-i}}a^{n-i}=\frac{(ab;q)_n}{(q;q)_n}$?

Published on
#binomial-theorem #q-series #q-analogs
435
Views

How to prove ${}_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n.$

Published on
#hypergeometric-function #q-analogs
166
Views

An identity for $q-$Fibonacci numbers if $q$ is a root of unity.

Published on
#reference-request #fibonacci-numbers #q-analogs
81
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Closed formula involving $q$-binomials

Published on
#combinatorics #binomial-coefficients #finite-fields #closed-form #q-analogs
412
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$q$-digamma function evaluation

Published on
#infinite-product #q-analogs
134
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Combinatorial identity. Using echelon matrices.

Published on
#linear-algebra #combinatorics #q-analogs
758
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What does the $q$-Catalan Numbers count?

Published on
#combinatorics #catalan-numbers #q-analogs #lagrange-inversion
638
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Example of something easier to count with $q$-analog?

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#combinatorics #q-analogs
999
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Intuition behind the Jacobi triple product

Published on
#combinatorics #number-theory #intuition #q-analogs

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