Question

Relation between the coefficients of Virial expansion and fugacity expansion?

score 24 · Answer 1 · 2023-06-05 14:40:15

24

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Relation between the coefficients of Virial expansion and fugacity expansion?

Published on 05 Jun 2023 - 14:40

score 78 · Answer 2 · 2026-03-30 05:13:22

78

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Variant of identity for a sum of binomial coefficient (Hockey-stick)

Published on 30 Mar 2026 - 5:13

score 43 · Answer 3 · 2026-03-30 09:51:41

43

Views

Why are the degrees of f(t) and g(z) related in this identity?

Published on 30 Mar 2026 - 9:51

score 403 · Answer 4 · 2026-03-26 08:04:03

403

Views

Bivariate generating function for squared binomial coefficients

Published on 26 Mar 2026 - 8:04

score 156 · Answer 5 · 2023-06-11 15:44:21

156

Views

Is $\sum_{s=n}^{m}\binom{m}{s}(x-1)^{m-s}=\sum_{s=n}^m\sum_{j=s}^m\binom{s-1}{n-1}\binom{m-s}{j-s}(x-1)^{m-j+s-n}$ an identity?

Published on 11 Jun 2023 - 15:44

score 112 · Answer 6 · 2023-06-11 17:21:37

112

Views

How to prove $\sum_{k=p}^n (-1)^k\binom{n}{k}\binom{k}{p} = (-1)^p$ by using generating functions

Published on 11 Jun 2023 - 17:21

score 79 · Answer 7 · 2023-06-11 18:27:06

79

Views

Non-homogenous recurrences using generating functions

Published on 11 Jun 2023 - 18:27

score 38 · Answer 8 · 2023-06-11 18:29:10

38

Views

Converting a power series with recursively related coefficients into a single sigma sum expression

Published on 11 Jun 2023 - 18:29

score 92 · Answer 9 · 2026-03-28 06:10:21

92

Views

Bijective proof for $\sum\limits_{\substack{n_1+n_2=n\\m_1+m_2=m}}\binom{n_1+m_1}{n_1}^2\binom{n_2+m_2}{n_2}^2=\frac{1}{2}\binom{2n+2m+2}{2n+1}$?

Published on 28 Mar 2026 - 6:10

score 57 · Answer 10 · 2023-06-15 18:25:57

57

Views

Exponential Generating Function for cooking recipe

Published on 15 Jun 2023 - 18:25

score 75 · Answer 11 · 2026-03-26 02:46:50

75

Views

Geometrical/Combinatorial interpretation of $ \pi = \frac{27}{4 \sqrt 3} \sum_2^∞ \frac{1}{C(k)} $

Published on 26 Mar 2026 - 2:46

score 110 · Answer 12 · 2026-03-26 09:19:51

110

Views

How to obtain explicit formula of coefficients for generating functions?

Published on 26 Mar 2026 - 9:19

score 63 · Answer 13 · 2026-04-02 09:17:38

63

Views

How to prove $\sum_{n\ge 0} a_n x^n = \sum_{n\ge 0} \left(\sum_{k=0}^{n}(-1)^{k+1} \binom{n}{k}a_k\right) \frac{x^n}{(x-1)^{n+1}}$?

Published on 02 Apr 2026 - 9:17

score 63 · Answer 14 · 2026-03-26 12:33:51

63

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Evaluate $\sum\limits_{n=0}^\infty\operatorname W(e^{e^{an}})x^n$ with Lambert W function

Published on 26 Mar 2026 - 12:33

score 106 · Answer 15 · 2023-06-22 10:00:27

106

Views

Is the below description a known formula/series?

Published on 22 Jun 2023 - 10:00

List Question

Relation between the coefficients of Virial expansion and fugacity expansion?

Variant of identity for a sum of binomial coefficient (Hockey-stick)

Why are the degrees of f(t) and g(z) related in this identity?

Bivariate generating function for squared binomial coefficients

Is $\sum_{s=n}^{m}\binom{m}{s}(x-1)^{m-s}=\sum_{s=n}^m\sum_{j=s}^m\binom{s-1}{n-1}\binom{m-s}{j-s}(x-1)^{m-j+s-n}$ an identity?

How to prove $\sum_{k=p}^n (-1)^k\binom{n}{k}\binom{k}{p} = (-1)^p$ by using generating functions

Non-homogenous recurrences using generating functions

Converting a power series with recursively related coefficients into a single sigma sum expression

Bijective proof for $\sum\limits_{\substack{n_1+n_2=n\\m_1+m_2=m}}\binom{n_1+m_1}{n_1}^2\binom{n_2+m_2}{n_2}^2=\frac{1}{2}\binom{2n+2m+2}{2n+1}$?

Exponential Generating Function for cooking recipe

Geometrical/Combinatorial interpretation of $ \pi = \frac{27}{4 \sqrt 3} \sum_2^∞ \frac{1}{C(k)} $

How to obtain explicit formula of coefficients for generating functions?

How to prove $\sum_{n\ge 0} a_n x^n = \sum_{n\ge 0} \left(\sum_{k=0}^{n}(-1)^{k+1} \binom{n}{k}a_k\right) \frac{x^n}{(x-1)^{n+1}}$?

Evaluate $\sum\limits_{n=0}^\infty\operatorname W(e^{e^{an}})x^n$ with Lambert W function

Is the below description a known formula/series?

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