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factoring infinite products of $q$-series with constant term equal to 1

score 166 · Answer 1 · 2026-04-12 00:50:37

166

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factoring infinite products of $q$-series with constant term equal to 1

Published on 12 Apr 2026 - 0:50

score 968 · Answer 2 · 2026-04-11 14:06:49

968

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Combinatorial interpretation of this identity of Gauss?

Published on 11 Apr 2026 - 14:06

score 6.5k · Answer 3 · 2026-05-11 05:37:28

6.5k

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Proving q-binomial identities

Published on 11 May 2026 - 5:37

score 449 · Answer 4 · 2026-04-17 07:03:12

449

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$\log P(e^{-2\pi t}) - \log P(e^{-2\pi /t}) = \frac{\pi}{12} \Bigl( \frac{1}{t} - t \Bigr)+ \frac{1}{2} \log t$

Published on 17 Apr 2026 - 7:03

score 1.6k · Answer 5 · 2026-04-16 13:10:10

1.6k

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Book Recommendation for Integer partitions and $q$ series

Published on 16 Apr 2026 - 13:10

score 798 · Answer 6 · 2026-04-13 13:24:37

798

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Show $1+\frac{8q}{1-q}+\frac{16q^2}{1+q^2}+\frac{24q^3}{1-q^3}+\dots=1+\frac{8q}{(1-q)^2}+\frac{8q^2}{(1+q^2)^2}+\frac{8q^3}{(1-q^3)^2}+\dots$.

Published on 13 Apr 2026 - 13:24

score 144 · Answer 7 · 2026-03-25 14:36:51

144

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Mellin transform of $\sin(\pi x)\left(\frac{d}{dx}\log\left(x;j^{-1}\right)\right)$

Published on 25 Mar 2026 - 14:36

score 58 · Answer 8 · 2026-04-14 19:54:10

58

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$q$-expansion of Klein's absolute invariant using infinite products

Published on 14 Apr 2026 - 19:54

score 96 · Answer 9 · 2026-03-25 14:36:41

96

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Is it true that $\frac 1q=\sum\limits_{\text{prime }p}^{\infty}\frac{1}{q^{p-1}-1}$ for all $q\notin[-1,1]$?

Published on 25 Mar 2026 - 14:36

score 162 · Answer 10 · 2026-05-10 20:07:17

162

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Modularity of Ramanujan-Sato series

Published on 10 May 2026 - 20:07

score 65 · Answer 11 · 2026-03-25 14:36:50

65

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Concerning the coefficient $[q^n]\sum_{n\ge1}\frac{(aq)^n}{(1-bq^n)^2}$.

Published on 25 Mar 2026 - 14:36

score 104 · Answer 12 · 2026-03-25 14:28:46

104

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Counting colored integer partitions with a strictness condition

Published on 25 Mar 2026 - 14:28

score 120 · Answer 13 · 2026-03-25 14:32:35

120

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Symbolic calculation vs. desmos

Published on 25 Mar 2026 - 14:32

score 74 · Answer 14 · 2026-03-25 14:34:39

74

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coefficient $[q^n]\sum_{m\ge1}\frac{q^{\alpha m}}{1-q^{\beta m}}$ where $0<\alpha<\beta$

Published on 25 Mar 2026 - 14:34

score 404 · Answer 15 · 2026-03-25 14:31:36

404

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Relation between Rogers Ramanujan continued fraction and $j$-invariant

Published on 25 Mar 2026 - 14:31

List Question

factoring infinite products of $q$-series with constant term equal to 1

Combinatorial interpretation of this identity of Gauss?

Proving q-binomial identities

$\log P(e^{-2\pi t}) - \log P(e^{-2\pi /t}) = \frac{\pi}{12} \Bigl( \frac{1}{t} - t \Bigr)+ \frac{1}{2} \log t$

Book Recommendation for Integer partitions and $q$ series

Show $1+\frac{8q}{1-q}+\frac{16q^2}{1+q^2}+\frac{24q^3}{1-q^3}+\dots=1+\frac{8q}{(1-q)^2}+\frac{8q^2}{(1+q^2)^2}+\frac{8q^3}{(1-q^3)^2}+\dots$.

Mellin transform of $\sin(\pi x)\left(\frac{d}{dx}\log\left(x;j^{-1}\right)\right)$

$q$-expansion of Klein's absolute invariant using infinite products

Is it true that $\frac 1q=\sum\limits_{\text{prime }p}^{\infty}\frac{1}{q^{p-1}-1}$ for all $q\notin[-1,1]$?

Modularity of Ramanujan-Sato series

Concerning the coefficient $[q^n]\sum_{n\ge1}\frac{(aq)^n}{(1-bq^n)^2}$.

Counting colored integer partitions with a strictness condition

Symbolic calculation vs. desmos

coefficient $[q^n]\sum_{m\ge1}\frac{q^{\alpha m}}{1-q^{\beta m}}$ where $0<\alpha<\beta$

Relation between Rogers Ramanujan continued fraction and $j$-invariant

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