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Determine all functions $f:\mathbb{Z}\to\mathbb{Z}$ such that $f\big(f(n)\big)=-(q-p)\,f(n)+pq\,n$ for all $n\in\mathbb{Z}$.

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#functions #recurrence-relations #functional-equations #recursion #integers
107
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Recurrence relation of binary string with given condition

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#recurrence-relations #bit-strings
46
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How to determine convergence of the sequence?

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#real-analysis #sequences-and-series #recurrence-relations
20
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How to find a particular solution for $a_{n}-a_{n-1}-6a_{n-2}=5\times3^n$

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#recurrence-relations
111
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Show that the sequence converges to a limit $L$

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#real-analysis #sequences-and-series #convergence-divergence #recurrence-relations
341
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How to show that this sequence is monotonic increasing?

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#real-analysis #sequences-and-series #recurrence-relations
46
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How to evaluate this limit involving matrices?

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#matrices #limits #recurrence-relations
65
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Solve Recurrence: $E(h) = \frac{1}{3} E(h-1) + \frac{2}{3} 2h$

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#discrete-mathematics #summation #recurrence-relations
71
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Linear difference equation with modulo operation

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#algorithms #recurrence-relations #integers
143
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Solve Recursive Function

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#sequences-and-series #discrete-mathematics #recurrence-relations
31
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Help with this recurrence

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#recurrence-relations
56
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Using Generating Functions to solve Recurrence Relation

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#combinatorics #recurrence-relations #generating-functions
168
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$ a_n = \frac{a_{n-1}(a_{n-1} + 1)}{a_{n-2}}.$ and $ T = 3.73205080..$?

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#real-analysis #limits #recurrence-relations #closed-form #rational-functions
51
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Prove a closed-form recurrence satisfies the original recurrence relation

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#discrete-mathematics #induction #recurrence-relations
30
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piecewise defining confusion

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#recurrence-relations #piecewise-continuity

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