       # small typo "in The Book"

```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

```

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