Question

difficulty for deriving the series representation of $f(x)=\frac{1+x^3}{(1+x)^3}$

score 175 · Answer 1 · 2024-02-17 18:57:01

175

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difficulty for deriving the series representation of $f(x)=\frac{1+x^3}{(1+x)^3}$

Published on 17 Feb 2024 - 18:57

score 171 · Answer 2 · 2024-02-21 12:13:12

171

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When a sequence satisfies $a_n= \sum_{i=1}^{n-1} f_i(n) a_i+ g(n)$?

Published on 21 Feb 2024 - 12:13

score 95 · Answer 3 · 2026-03-28 10:16:30

95

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Counting the number of possible sequences increasing by no more than one

Published on 28 Mar 2026 - 10:16

score 766 · Answer 4 · 2024-02-22 08:36:55

766

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How to put 6 rooks which they wont' attack each other?

Published on 22 Feb 2024 - 8:36

score 124 · Answer 5 · 2026-03-25 11:25:58

124

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How to come up with the generating function of an elliptic curve?

Published on 25 Mar 2026 - 11:25

score 77 · Answer 6 · 2024-02-22 23:04:07

77

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Combinatorics - rewriting generating function as power series

Published on 22 Feb 2024 - 23:04

score 50 · Answer 7 · 2024-02-24 04:36:39

50

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Justification for the generating function equality in the derivation of the Bernoulli-Seki formula

Published on 24 Feb 2024 - 4:36

score 70 · Answer 8 · 2026-02-23 07:13:12

70

Views

Exponential Generating Function for Dirichlet Character

Published on 23 Feb 2026 - 7:13

score 130 · Answer 9 · 2024-02-25 19:04:19

130

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Exponential generating function of the sequence $1,0,1,0,\dots$

Published on 25 Feb 2024 - 19:04

score 39 · Answer 10 · 2024-02-26 07:37:29

39

Views

Finding a pole by using a fixed point iteration

Published on 26 Feb 2024 - 7:37

score 32 · Answer 11 · 2026-03-30 20:56:01

32

Views

Is it possible to derive the identity $F_{n+1} = \sum_{k=0}^{n}\binom{n-k}{k}$ from the generating function $F(x) = \frac{x}{(1-x-x^2)}$

Published on 30 Mar 2026 - 20:56

score 108 · Answer 12 · 2026-04-02 05:20:53

108

Views

Using Generator functions to solve following recursive formulas

Published on 02 Apr 2026 - 5:20

score 294 · Answer 13 · 2026-03-26 06:25:33

294

Views

Closed form for infinite sum involving Chebyshev polynomials

Published on 26 Mar 2026 - 6:25

score 32 · Answer 14 · 2026-03-30 18:12:05

32

Views

Generating Function for Hypergeometric Polynomials

Published on 30 Mar 2026 - 18:12

score 47 · Answer 15 · 2026-03-26 12:49:20

47

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Morse and Fesbach identity $\sum_{n=0}^{\infty} e^{-(n+\frac{1}{2})|u|} \; P_n(x) =(2\cosh u - 2x)^{-1/2}$

Published on 26 Mar 2026 - 12:49

List Question

difficulty for deriving the series representation of $f(x)=\frac{1+x^3}{(1+x)^3}$

When a sequence satisfies $a_n= \sum_{i=1}^{n-1} f_i(n) a_i+ g(n)$?

Counting the number of possible sequences increasing by no more than one

How to put 6 rooks which they wont' attack each other?

How to come up with the generating function of an elliptic curve?

Combinatorics - rewriting generating function as power series

Justification for the generating function equality in the derivation of the Bernoulli-Seki formula

Exponential Generating Function for Dirichlet Character

Exponential generating function of the sequence $1,0,1,0,\dots$

Finding a pole by using a fixed point iteration

Is it possible to derive the identity $F_{n+1} = \sum_{k=0}^{n}\binom{n-k}{k}$ from the generating function $F(x) = \frac{x}{(1-x-x^2)}$

Using Generator functions to solve following recursive formulas

Closed form for infinite sum involving Chebyshev polynomials

Generating Function for Hypergeometric Polynomials

Morse and Fesbach identity $\sum_{n=0}^{\infty} e^{-(n+\frac{1}{2})|u|} \; P_n(x) =(2\cosh u - 2x)^{-1/2}$

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