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 October 23rd, 2018, 10:07 PM #1 Member   Joined: Aug 2018 From: România Posts: 88 Thanks: 6 A recurrence equation Hello everybody, Solve the recurrence equation $\displaystyle |f(x^2+1)-f(x^2-1)|=3x^2+2x+1$. All the best, Integrator October 24th, 2018, 05:58 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 What do you mean by "recurrence equation"? October 24th, 2018, 01:04 PM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 First be sure $\displaystyle f(x^2 +1)$ and $\displaystyle f(x^2 -1)$ is a polynomial function October 24th, 2018, 01:14 PM #4 Member   Joined: Oct 2018 From: Netherlands Posts: 39 Thanks: 3 Probably meant is a "recurrence relation" which is a type of equation defining a function through recursion. Explains why the polynomial is missing. https://en.wikipedia.org/wiki/Recurrence_relation Last edited by Arisktotle; October 24th, 2018 at 01:31 PM. October 24th, 2018, 09:39 PM   #5
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Quote:
 Originally Posted by skipjack What do you mean by "recurrence equation"?
Hello,

Recurrence Equation -- from Wolfram MathWorld

All the best,

Integrator October 25th, 2018, 06:59 AM   #6
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Quote:
 Originally Posted by idontknow First be sure $\displaystyle f(x^2 +1)$ and $\displaystyle f(x^2 -1)$ is a polynomial function
Why? As a trivial counter-example, what if $\displaystyle f(x^2 + 1) = x^2 - 1 + ln(x)$ and $\displaystyle f(x^2 - 1) = 3x + 5 + ln(x)$?

-Dan October 25th, 2018, 08:34 PM   #7
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Quote:
 Originally Posted by topsquark Why? As a trivial counter-example, what if $\displaystyle f(x^2 + 1) = x^2 - 1 + ln(x)$ and $\displaystyle f(x^2 - 1) = 3x + 5 + ln(x)$? -Dan
Hello,

If $\displaystyle f(x^2 + 1) = x^2 - 1 + ln(x)$ and $\displaystyle f(x^2 - 1) = 3x + 5 + ln(x)$ , then what expression has $\displaystyle f(x)$?Thank you very much!

All the best,

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