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New posts in q-series
Show $1+\frac{8q}{1-q}+\frac{16q^2}{1+q^2}+\frac{24q^3}{1-q^3}+\dots=1+\frac{8q}{(1-q)^2}+\frac{8q^2}{(1+q^2)^2}+\frac{8q^3}{(1-q^3)^2}+\dots$.
sequences-and-series
complex-analysis
q-series
double-sequence
Show that $\prod\limits_{n=1}^\infty \frac{(1-q^{6n})(1-q^n)^2}{(1-q^{3n})(1-q^{2n})}=\sum\limits_{n=-\infty}^\infty q^{2n^2+n}-3q^{9(2n^2+n)+1}$.
modular-forms
theta-functions
q-series
Proving that odd partitions and distinct partitions are equal
sequences-and-series
generating-functions
infinite-product
integer-partitions
q-series
a conjecture of certain q-continued fractions
number-theory
continued-fractions
conjectures
q-series
A problem with the geometric series and matrices?
matrices
inverse
q-series
Does the Rogers-Ramanujan continued fraction $R(q)$ satisfy this conjectured infinite series
number-theory
continued-fractions
modular-forms
conjectures
q-series
Closed form of the integral ${\large\int}_0^\infty e^{-x}\prod_{n=1}^\infty\left(1-e^{-24\!\;n\!\;x}\right)dx$
calculus
integration
definite-integrals
infinite-product
q-series
the ratio of jacobi theta functions and a new conjectured q-continued fraction
continued-fractions
conjectures
theta-functions
q-series
Combinatorial interpretation of this identity of Gauss?
combinatorics
theta-functions
q-series
The ratio of jacobi theta functions
special-functions
modular-forms
continued-fractions
q-series
Why $e^{\pi}-\pi \approx 20$, and $e^{2\pi}-24 \approx 2^9$?
power-series
approximation
pi
laurent-series
q-series
a new continued fraction for $\sqrt{2}$
number-theory
modular-forms
continued-fractions
q-series
Ramanujan theta function and its continued fraction
number-theory
modular-forms
continued-fractions
theta-functions
q-series
Motivation for/history of Jacobi's triple product identity
sequences-and-series
math-history
motivation
q-series
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