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15
Math.TechQA.Club
2026-02-28 03:01:28
102
Views
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
28 Feb 2026 - 3:01
#binomial-theorem
#q-series
#q-analogs
136
Views
a conjecture of two equivalent q-continued fractions related to the reciprocal of the Göllnitz-Gordon continued fraction A111374-OEIS
Published on
05 Nov 2015 - 14:15
#number-theory
#modular-forms
#continued-fractions
#conjectures
#q-series
726
Views
Closed form of the integral ${\large\int}_0^\infty e^{-x}\prod_{n=1}^\infty\left(1-e^{-24\!\;n\!\;x}\right)dx$
Published on
22 Nov 2015 - 19:29
#calculus
#integration
#definite-integrals
#infinite-product
#q-series
1.7k
Views
Why $e^{\pi}-\pi \approx 20$, and $e^{2\pi}-24 \approx 2^9$?
Published on
03 Jan 2016 - 18:33
#power-series
#approximation
#pi
#laurent-series
#q-series
104
Views
Weighted Q-binomial Coefficients
Published on
13 Mar 2016 - 1:01
#combinatorics
#generating-functions
#analytic-number-theory
#hypergeometric-function
#q-series
55
Views
show $\sum_{j=0}^n (-1)^j {n \brack j}_q =0$ for n odd
Published on
29 Mar 2016 - 11:18
#combinatorics
#integer-partitions
#q-series
#pochhammer-symbol
77
Views
A q-series related to adjoint representation of lie group
Published on
28 Jun 2013 - 23:34
#abstract-algebra
#q-series
4k
Views
Motivation for/history of Jacobi's triple product identity
Published on
03 Jul 2013 - 1:07
#sequences-and-series
#math-history
#motivation
#q-series
375
Views
q-series identities
Published on
24 Mar 2026 - 21:48
#q-series
145
Views
Q-series identities #2
Published on
24 Mar 2026 - 18:47
#q-series
625
Views
Combinatorial Identity $ \sum_{k=1}^n (-1)^{k-1} \cdot q^{\frac{k(k-1)}{2}} \cdot \frac{\prod_{i=n-k+1}^n(1-q^i)}{\prod_{i=1}^k(1-q^i)} = 1 $
Published on
11 Dec 2013 - 14:11
#combinatorics
#binomial-coefficients
#q-series
#pochhammer-symbol
3.8k
Views
A problem with the geometric series and matrices?
Published on
12 Dec 2013 - 23:11
#matrices
#inverse
#q-series
180
Views
Ramanujan Notebook Part 1 (1.16): $\sum q^{n^2} = (-q;q^2)_\infty^2(q^2;q^2)_\infty=\frac{(-q;-q)_\infty}{(q;-q)_\infty}$
Published on
01 Jan 2014 - 23:19
#number-theory
#summation
#generating-functions
#q-series
348
Views
$q$-series identity
Published on
24 Mar 2026 - 19:52
#q-series
301
Views
Differentiating q-Series Expression
Published on
16 Apr 2017 - 18:12
#sequences-and-series
#derivatives
#infinite-product
#q-series
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