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 May 18th, 2019, 08:38 AM #1 Senior Member   Joined: Aug 2018 From: România Posts: 112 Thanks: 7 An equation of recurrence Hello all, Solve the recurrence equation $\displaystyle f''(x-2)+f''(x)+f''(x+2)=2f''(x+1)$. All the best, Integrator
 May 18th, 2019, 02:17 PM #2 Global Moderator   Joined: May 2007 Posts: 6,855 Thanks: 744 Simplest solution f''(x)=0.
May 18th, 2019, 09:53 PM   #3
Senior Member

Joined: Aug 2018
From: România

Posts: 112
Thanks: 7

Quote:
 Originally Posted by mathman Simplest solution f''(x)=0.
Hello,

Others say they are solutions and if
$\displaystyle f''(x)=c_1\bigg(\frac{1-\sqrt{1-4i}}{2}\bigg)^x+c_2\bigg(\frac{1+\sqrt{1-4i}}{2}\bigg)^x+c_3\bigg(\frac{1-\sqrt{1+4i}}{2}\bigg)^x+c_4\bigg(\frac{1+\sqrt{1+4 i}}{2}\bigg)^x$
where $\displaystyle i^2=-1$ and $\displaystyle c_1$ , $\displaystyle c_2$ , $\displaystyle c_3$ , $\displaystyle c_4$ are constants.
Is it right what others say? Thank you very much!

All the best,

Integrator

Last edited by skipjack; May 18th, 2019 at 10:57 PM.

 May 18th, 2019, 10:55 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,124 Thanks: 2332 Yes. Thanks from Integrator

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