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April 11th, 2015, 10:39 PM   #1
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Recurrence equation

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Solve the recurrence equation $\displaystyle a'_{n}-a_{n-1}+n^2-2n=0$.
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April 11th, 2015, 11:58 PM   #2
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What does $a'_{n}$ mean?
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April 12th, 2015, 06:20 AM   #3
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Quote:
Originally Posted by skipjack View Post
What does $a'_{n}$ mean?
First derivative of $\displaystyle a_{n}$
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April 12th, 2015, 07:04 AM   #4
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First derivative with respect to what?
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April 12th, 2015, 08:16 PM   #5
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Quote:
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First derivative with respect to what?
$\displaystyle a_{n}=f(n)$ and so $\displaystyle a'_{n}=f'(n)$.
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April 13th, 2015, 05:57 AM   #6
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A priori, f(n) is discrete and has no derivative.
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April 13th, 2015, 11:04 AM   #7
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Maybe this definition of a derivate was intended: Arithmetic derivative - OeisWiki
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April 13th, 2015, 07:07 PM   #8
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If $a_n$ has to be a polynomial, $a_n = n^2 + 2n + 3$ and $a'_n = 2n + 2$, the equation is satisfied.
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April 13th, 2015, 08:00 PM   #9
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Quote:
Originally Posted by skipjack View Post
If $a_n$ has to be a polynomial, $a_n = n^2 + 2n + 3$ and $a'_n = 2n + 2$, the equation is satisfied.
Correctly!There are other expressions for $\displaystyle a_{n}$?
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