small typo "in The Book"
- To: mathgroup@smc.vnet.net
- Subject: [mg10556] small typo "in The Book"
- From: Wouter Meeussen <eu000949@pophost.eunet.be>
- Date: Tue, 20 Jan 1998 16:54:00 -0500
Mathematical Functions > Combinatorial > Fibonacci
The Fibonacci polynomial F[n,x] is the coefficient of
t^n in the expansion of t/(1 - x t - t^2)
*** the above is ok, but, below, it is wrong : ***
3.2.5 Combinatorial Functions
The Fibonacci polynomials Fibonacci[n, x] appear as the coefficients of
t^n in the expansion of
t/(1 - x t - t^2) = Sum[ F[n,x] t^n /n! ,{n,0,Infinity}]
^^^
^^^ *** check : ***
Simplify/@Normal[Series[t/(1-x t-t^2),{t,0,6}]] t + t^2*x + t^3*(1 +
x^2) + t^4*x*(2 + x^2) + t^5*(1 + 3*x^2 + x^4) +
t^6*x*(3 + 4*x^2 + x^4)
Simplify/@Sum[ Fibonacci[n,x] t^n ,{n,0,6}] t + t^2*x + t^3*(1 +
x^2) + t^4*x*(2 + x^2) + t^5*(1 + 3*x^2 + x^4) +
t^6*x*(3 + 4*x^2 + x^4)
*** a different matter is whether
Sum[Fibonacci[n,x] t^n,{n,0,Infinity}]//FullSimplify
should evaluate to t/(1 - x t - t^2) , and whether or not
it would be "used" by FullSimplify if given as downvalue to
Fibonacci. ***
wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc@vandemoortele.be
eu000949@pophost.eunet.be