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Is there another way to prove this expression over $1/(1-z)$

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#sequences-and-series #combinatorics #generating-functions
96
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Converting recurrence involving binomial terms and generating functions to closed form.

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#sequences-and-series #summation #binomial-coefficients #generating-functions #catalan-numbers
459
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General form for this problem

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#sequences-and-series #combinatorics #power-series #generating-functions
182
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Generating function for convolution over odd/even indices only

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#recurrence-relations #generating-functions #convolution
35
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Generating function of a discrete variable

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#probability #probability-distributions #random-variables #generating-functions
416
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Independence of two random variables (by checking joint generating function)

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#probability-theory #random-variables #solution-verification #generating-functions #independence
96
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(Feller Vol.1) the generating function for the probabilities that the event $S_n = r$ will occur exactly $k$ times

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#probability-theory #stochastic-processes #generating-functions
34
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Generating function problem follow

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#combinatorics #discrete-mathematics #generating-functions
1.1k
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Determine sequence with generating function $(2x-3)^3$

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#discrete-mathematics #generating-functions
295
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Any Info on Generalized Binomial and Exponential Series?

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#generating-functions
174
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Find the coefficient of $x^{31}$ in $(1+x+x^2+x^3+\ldots)^k$

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#discrete-mathematics #polynomials #generating-functions
33
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What is the closed form of the generating function of the solution to a linear recurrence?

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#recurrence-relations #generating-functions #closed-form
340
Views

Find generating function for $F_{2n}$

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#discrete-mathematics #generating-functions #fibonacci-numbers
63
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Prove that $\sum_nF_{2n+1}x^n=\frac{1-x}{1-3x+x^2}$

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#discrete-mathematics #generating-functions #fibonacci-numbers
79
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Any hints for analysing $\prod_{i=1}^n\big(1 + \alpha(-1)^i/\sqrt i\big)$?

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#optimization #asymptotics #generating-functions #products

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