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Coefficient in Formal Power Seies

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#sequences-and-series #combinatorics #generating-functions
93
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Finding generating function and closed formula

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#solution-verification #generating-functions
61
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n-th element of a recursive section with complex roots

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#discrete-mathematics #recurrence-relations #generating-functions
152
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Rising factorial stirling numbers from the recurrence

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#combinatorics #recurrence-relations #generating-functions #stirling-numbers
142
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Summation over $a+b+c=5$

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#discrete-mathematics #summation #generating-functions
114
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Under what conditions is $\sum_{n\ge0}a_nx^n\ge\sum_{n\ge0}b_nx^n\Rightarrow a_n\ge b_n$ true?

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#real-analysis #sequences-and-series #inequality #generating-functions #functional-inequalities
49
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Recurrence with Bernoulli-Barnes Polynomials

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#number-theory #recurrence-relations #generating-functions #bernoulli-polynomials
107
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Re-arranging and integrating a Generating Function of Legendre Polynomials

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#integration #generating-functions #legendre-polynomials
529
Views

Closed form expression for the series $\sum n!/n^n$

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#sequences-and-series #convergence-divergence #power-series #generating-functions
149
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Generating Function for a random variable

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#probability-theory #convergence-divergence #stochastic-processes #generating-functions
290
Views

Solving a recurrence relation - confusion about partial fraction decomposition

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#recurrence-relations #generating-functions #partial-fractions
43
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Show that $\prod_{i=1}^n\frac{z-tx_i}{z-x_i}=1+\sum_{i=1}^n\frac{(1-t)x_i}{z-x_i}\prod_{\substack{j\ne i,\\j\in [n]}}\frac{x_i-tx_j}{x_i-x_j}.$

Published on
#combinatorics #induction #generating-functions #symmetric-functions
48
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Differential of a generating function

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#derivatives #generating-functions
126
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On Finding the Limit of a recurrence relation.

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#sequences-and-series #algebra-precalculus #convergence-divergence #recurrence-relations #generating-functions
50
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$q$-analog generalization for limits not going to 1

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#combinatorics #reference-request #generating-functions #q-analogs

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