Re: fibonacci question
- To: mathgroup at smc.vnet.net
- Subject: [mg119467] Re: fibonacci question
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Sun, 5 Jun 2011 07:03:14 -0400 (EDT)
- References: <isd0r7$1m2$1@smc.vnet.net>
On 04/06/2011 11:19, olfa wrote: > Hello Mathematica community, > > why FullSimplify[Fibonacci[cn] + Fibonacci[cn + 1]] is not simplified > into Fibonacci[cn+2]? > what mathematica function should I use to get this output? > > thank you very much for your help. > You cannot expect FullSimplify to use every mathematical fact in every possible way. If are working with Fibonacci, and need this simplification, one way is to use a transformation rule: Fibonacci[cn] + Fibonacci[cn + 1]/.Fibonacci[x_]+Fibonacci[y_]:>Fibonacci[y+1]/;y==x+1 Note that this is a bit more general, in that it will also spot expressions like Fibonacci[cn-1] + Fibonacci[cn]. It doesn't depend on the order in which things are summed, and the sum can contain other terms as well: In[635]:= Fibonacci[cn-1] + cn-1+Fibonacci[cn-2]/.Fibonacci[x_]+Fibonacci[y_]:>Fibonacci[y+1]/;y==x+1 Out[635]= -1 + cn + Fibonacci[cn] David Bailey http://www.dbaileyconsultancy.co.uk