Complex Analysis Complex Analysis Math Forum

 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 Tags equation, recurrence Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Integrator Algebra 6 October 25th, 2018 09:34 PM Dacu Real Analysis 8 April 13th, 2015 09:00 PM One Real Analysis 2 June 17th, 2013 02:20 PM Oscarmovies Computer Science 2 March 1st, 2013 11:54 PM mathbalarka Algebra 2 July 8th, 2012 12:43 AM

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