Question

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

score 164 · Answer 1 · 2026-03-25 14:34:36

164

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

Published on 25 Mar 2026 - 14:34

score 92 · Answer 2 · 2012-11-27 01:49:42

92

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Definition domains of the pochhammer symbols?

Published on 27 Nov 2012 - 1:49

score 35 · Answer 3 · 2020-08-08 18:12:05

35

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Writing $(a)_k*(a)_k$ as one Pochhammer Symbol or in terms of one Gamma ($\Gamma$) function?

Published on 08 Aug 2020 - 18:12

score 68 · Answer 4 · 2020-08-13 14:16:37

68

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hypergeometric function in terms of Pochammer polynomials

Published on 13 Aug 2020 - 14:16

score 337 · Answer 5 · 2020-11-27 18:25:07

337

Views

show $ {-a\choose k} = \frac{(-1)^k (a)_{k}}{k!} $

Published on 27 Nov 2020 - 18:25

score 70 · Answer 6 · 2020-12-13 21:12:29

70

Views

Proof that the set of Pochhammer numbers satisfies Benford's law

Published on 13 Dec 2020 - 21:12

score 127 · Answer 7 · 2021-01-30 20:01:42

127

Views

Show that $\frac{1}{(-q,q)_\infty}=(q,q^2)_\infty$

Published on 30 Jan 2021 - 20:01

score 26 · Answer 8 · 2021-01-30 22:31:53

26

Views

Prove that $\sum_{-\infty}^{\infty}\frac{(a;q)_nt^n}{(b;q)_n}$ is an analytic funciton in $b$.

Published on 30 Jan 2021 - 22:31

score 95 · Answer 9 · 2021-02-01 18:36:22

95

Views

Limiting behaviour between ratio $q$-Pochhammer symbol and $n$'th coefficient

Published on 01 Feb 2021 - 18:36

score 126 · Answer 10 · 2021-03-13 15:00:58

126

Views

Integrating the Pochhammer symbol. $\int_{-1}^{1} \prod_{j=0}^{\infty} (1-x^{j+1})$

Published on 13 Mar 2021 - 15:00

score 356 · Answer 11 · 2021-04-03 20:16:28

356

Views

Asymptotic expansion of q-Pochhammer symbol near q = 1

Published on 03 Apr 2021 - 20:16

score 62 · Answer 12 · 2021-05-04 15:43:45

62

Views

Convergence of asymptotic series for $z^k/(z)_k$, $z\to\infty$

Published on 04 May 2021 - 15:43

score 205 · Answer 13 · 2021-06-05 01:10:36

205

Views

Looking for a Hypergeometric Function Related to Appell Series

Published on 05 Jun 2021 - 1:10

score 70 · Answer 14 · 2021-06-11 11:09:11

70

Views

On the decimal expansion of $\prod_{k=1}^{\infty} \sum_{\ell =1}^{k} \frac{9}{10^\ell}$

Published on 11 Jun 2021 - 11:09

score 96 · Answer 15 · 2021-06-23 01:30:35

96

Views

Proof the equality $\prod_{r=1}^{mn}\left(x+mn -r\right)=\prod_{k=1}^{m}\prod_{l=1}^{n}\left(x+mn-(1+ml-k) \right)$

Published on 23 Jun 2021 - 1:30

List Question

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

Definition domains of the pochhammer symbols?

Writing $(a)_k*(a)_k$ as one Pochhammer Symbol or in terms of one Gamma ($\Gamma$) function?

hypergeometric function in terms of Pochammer polynomials

show $ {-a\choose k} = \frac{(-1)^k (a)_{k}}{k!} $

Proof that the set of Pochhammer numbers satisfies Benford's law

Show that $\frac{1}{(-q,q)_\infty}=(q,q^2)_\infty$

Prove that $\sum_{-\infty}^{\infty}\frac{(a;q)_nt^n}{(b;q)_n}$ is an analytic funciton in $b$.

Limiting behaviour between ratio $q$-Pochhammer symbol and $n$'th coefficient

Integrating the Pochhammer symbol. $\int_{-1}^{1} \prod_{j=0}^{\infty} (1-x^{j+1})$

Asymptotic expansion of q-Pochhammer symbol near q = 1

Convergence of asymptotic series for $z^k/(z)_k$, $z\to\infty$

Looking for a Hypergeometric Function Related to Appell Series

On the decimal expansion of $\prod_{k=1}^{\infty} \sum_{\ell =1}^{k} \frac{9}{10^\ell}$

Proof the equality $\prod_{r=1}^{mn}\left(x+mn -r\right)=\prod_{k=1}^{m}\prod_{l=1}^{n}\left(x+mn-(1+ml-k) \right)$

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