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May 18th, 2019, 07:38 AM   #1
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An equation of recurrence

Hello all,

Solve the recurrence equation $\displaystyle f''(x-2)+f''(x)+f''(x+2)=2f''(x+1)$.

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May 18th, 2019, 01:17 PM   #2
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Simplest solution f''(x)=0.
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May 18th, 2019, 08:53 PM   #3
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Quote:
Originally Posted by mathman View Post
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!

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Last edited by skipjack; May 18th, 2019 at 09:57 PM.
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May 18th, 2019, 09:55 PM   #4
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Yes.
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