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Curious closed forms of the $q$-Gamma function.

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#special-functions #analytic-number-theory #closed-form #infinite-product #q-analogs
129
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Coefficients of polynomial $f_n(q)=\prod_{k=1}^{n}(1+q^k)$

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#sequences-and-series #analytic-number-theory #products #infinite-product #q-analogs
522
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Why is the "q-Pochhammer Symbol" referred to as such, despite not being a q-analog of the Pochhammer symbol?

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#combinatorics #q-analogs #pochhammer-symbol
688
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A question on a sum of $q$-binomial coefficients

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#summation #q-analogs #q-series
306
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Prove identity involving the Tsallis q-logarithm

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#sequences-and-series #entropy #q-analogs
122
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Roots of derivative of q-expontial function

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#sequences-and-series #derivatives #exponential-function #roots #q-analogs
223
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Infinite sum involving $q$-adic representations of whole numbers and $q$-factorial numbers

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#combinatorics #elementary-number-theory #reference-request #arithmetic #q-analogs
420
Views

Gaussian binomial coefficients, lattice paths, and vector spaces

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#probability #combinatorics #finite-fields #q-analogs
57
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Studying quantized algebras, why introduce $q^{1/2}$ instead of just $q$?

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#representation-theory #quantum-groups #q-analogs #quantum-calculus
93
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Why is $q$ sometimes a complex number, but other times a prime power?

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#representation-theory #quantum-groups #q-analogs #quantum-calculus
62
Views

An identity for generalized q-Fibonacci polynomials

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#combinatorics #q-analogs
302
Views

Area under a lattice path, from q-binomial to q-multinomial

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#combinatorics #number-theory #q-analogs
257
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$q$-analogue of $\sum_{k=0}^n \, {n \choose k} = 2^n $

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#combinatorics #elementary-number-theory #binomial-coefficients #binomial-theorem #q-analogs
208
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What are the asymptotics of the $q$-binomial?

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#combinatorics #asymptotics #binomial-coefficients #symmetric-functions #q-analogs
165
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Calculate $\sum_{ k = 1 } ^ n \ln ( 1 - x ^ k )$

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#summation #logarithms #q-analogs #pochhammer-symbol

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