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 April 11th, 2015, 10:39 PM #1 Senior Member   Joined: Apr 2013 Posts: 425 Thanks: 24 Recurrence equation Hello! Solve the recurrence equation $\displaystyle a'_{n}-a_{n-1}+n^2-2n=0$.
 April 11th, 2015, 11:58 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,929 Thanks: 2205 What does $a'_{n}$ mean?
April 12th, 2015, 06:20 AM   #3
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Quote:
 Originally Posted by skipjack What does $a'_{n}$ mean?
First derivative of $\displaystyle a_{n}$

 April 12th, 2015, 07:04 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,929 Thanks: 2205 First derivative with respect to what?
April 12th, 2015, 08:16 PM   #5
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Quote:
 Originally Posted by skipjack First derivative with respect to what?
$\displaystyle a_{n}=f(n)$ and so $\displaystyle a'_{n}=f'(n)$.

 April 13th, 2015, 05:57 AM #6 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms A priori, f(n) is discrete and has no derivative.
 April 13th, 2015, 11:04 AM #7 Math Team   Joined: Apr 2010 Posts: 2,780 Thanks: 361 Maybe this definition of a derivate was intended: Arithmetic derivative - OeisWiki
 April 13th, 2015, 07:07 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,929 Thanks: 2205 If $a_n$ has to be a polynomial, $a_n = n^2 + 2n + 3$ and $a'_n = 2n + 2$, the equation is satisfied.
April 13th, 2015, 08:00 PM   #9
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Quote:
 Originally Posted by skipjack 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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