List questions from generating-functions

Published on 28 Mar 2026 - 6:09

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Intuition behind this Olympiad problem using generating functions

Published on 26 Mar 2026 - 10:57

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Expanding a potential function via the generating function for Legendre polynomials

Published on 25 Mar 2026 - 23:35

421

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Exponential generating functions balls problem

Published on 11 Aug 2016 - 12:05

350

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Prove $\sum\limits_l\frac{R^{2l+1}r^{-l-1}P_l(\cos\theta)}{a^{l+1}}=\frac{R}{a\sqrt{(R^2/a)^2-2r\cos\theta (R^2/a)+r^2}}$ from LHS $\to$ RHS

Published on 26 Mar 2026 - 1:12

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Find the value $P_n(1)$ of the Legendre polynomials from their generating function

Published on 25 Mar 2026 - 23:36

182

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Problem solving recurrence equation for $a_n = a_{n-1} + 2a_{n-2}, \,\,\, a_0=a_1=1$

Published on 17 Aug 2016 - 9:11

55

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How do I get the closed form of this recurrence using generating functions?

Published on 24 Aug 2016 - 15:54

515

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A Polynomial Recurrence relation

Published on 26 Aug 2016 - 16:51

88

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Different ways to solve a number sequencing problem

Published on 26 Mar 2026 - 11:16

139

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A nice identity involving urns and balls problem

Published on 01 Sep 2016 - 5:37

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A sequence of coefficients of $x+(x+(x+(x+(x+(x+\dots)^6)^5)^4)^3)^2$

Published on 26 Mar 2026 - 8:23

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Determine Coefficient from Generating Functions

Published on 04 Sep 2016 - 1:36

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Counting free trees from rooted trees.

Published on 05 Sep 2016 - 13:15

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Solving $\sum_{k=0}^n 2^k \binom{2n-k}{n}=4^n$ using generating functions

Published on 06 Sep 2016 - 12:50

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Intuition behind this Olympiad problem using generating functions

Expanding a potential function via the generating function for Legendre polynomials

Exponential generating functions balls problem

Prove $\sum\limits_l\frac{R^{2l+1}r^{-l-1}P_l(\cos\theta)}{a^{l+1}}=\frac{R}{a\sqrt{(R^2/a)^2-2r\cos\theta (R^2/a)+r^2}}$ from LHS $\to$ RHS

Find the value $P_n(1)$ of the Legendre polynomials from their generating function

Problem solving recurrence equation for $a_n = a_{n-1} + 2a_{n-2}, \,\,\, a_0=a_1=1$

How do I get the closed form of this recurrence using generating functions?

A Polynomial Recurrence relation

Different ways to solve a number sequencing problem

A nice identity involving urns and balls problem

A sequence of coefficients of $x+(x+(x+(x+(x+(x+\dots)^6)^5)^4)^3)^2$

Determine Coefficient from Generating Functions

Counting free trees from rooted trees.

Solving $\sum_{k=0}^n 2^k \binom{2n-k}{n}=4^n$ using generating functions

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