Use this tag for questions pretaining to q-analogs of functions, for example q-Binomials, $q$-derivatives, the q-theta function, the q-Pochammer symbol, etc.

learn more… | top users | synonyms

1
vote
1answer
39 views

Good article or book to q-analogs?

I want to learn more about the following Topics: $q$-analog calculus what can be done with the $q$-Pochhammer Symbol applications of $q$-analogs in combinatorics However, I have found very Little ...
9
votes
0answers
204 views

Different notions of q-numbers

It seems that most of the literature dealing with q-analogs defines q-numbers according to $$[n]_q\equiv \frac{q^n-1}{q-1}.$$ Even Mathematica uses this definition: with the built-in function QGamma ...
7
votes
0answers
148 views

Infinite sum involving $q$-adic representations of whole numbers and $q$-factorial numbers

Let $q \in \mathbb{N}_{\geq 2}$. For $n \in \mathbb{N}_0$, let $$\mathrm{fac}_q(n) := \prod_{i=1}^n (1+q+\dots+q^{i-1}) = \prod_{i=1}^n \frac{q^i-1}{q-1}$$ be the $q$-factorial of $n$. In particular, ...
4
votes
0answers
128 views

A general Combinatorics problem (Coefficients of the q factorial)

I was solving a combinatorics problem when I encountered difficulties. The problem was: $x_1 \in \{0,1\}$ $x_2 \in \{0,1,2\}$ . . $x_{n-1}\in\{0,1,2..,n-1\}$ We have to find the number of ways ...
4
votes
0answers
62 views

Necessary and sufficient condition for $f(q^n)$ to be in $\mathbb{Z}[q,q^{-1}]$ when $f\in\mathbb{Q}(q)[x]$?

In this question, user begins shows that, for each $k\in \mathbb{N}$, there is a unique polynomial $P_k(x)$ of degree $k$ whose coefficients are in $\mathbb{Q}(q)$, the field of rational functions, ...
2
votes
0answers
28 views

Barnes' double gamma function versus q-gamma function

According to wikipedia, the q-analog of the gamma function is closely related to a multiple gamma function defined by Barnes. Besides the fact that they are both generalizations of the Gamma function, ...
0
votes
0answers
23 views

when cdf=( i-0.5)/n and you have a negative

I am stuck with when you set your cdf to equal $\frac{i-0.5}{n}$ for when you are plotting QQ plots. I have: $$-e^{\frac{-x^2}{2\sigma^2}}= \frac{i-0.5}{n}$$ Then I got stuck because I need to take ...
0
votes
0answers
19 views

About q-analogs

I am interested in learning the foundation of the calculus with q-analogs. I have read that the q-analog (analysis) is used in combinatorics. However, I didn't find much pdf or wiki artices that ...