[R] taylor expansions with real vectors

[Petr Savicky]

On Wed, Jul 18, 2012 at 06:02:27PM -0700, bilelsan wrote:
> Leave the Taylor expansion aside, how is it possible to compute with [R]:
> f(e) = e1 + e2 #for r = 1 
> + 1/2!*e1^2 + 1/2!*e2^2 + 1/2!*e1*e2 #for r = 2, excluding e2*e1 
> + 1/3!*e1^3 + 1/3!*e1^2*e2 + 1/3!*e2^2*e1 + 1/3!*e2^3 #for r = 3, excluding
> e2*e1^2 and e1*e2^2 
> + ... #for r = k
> In other words, I am trying to figure out how to compute all the possible
> combinations as exposed above.

Hi.

For a general r, do you mean the following sum of products?

  1/r! (e1^r + e1^(r-1) e2 + ... e1 e2^(r-1) + e2^r)

If this is correct, then try

  f <- 0
  for (r in 1:k) {
     f <- f + 1/factorial(r) * sum(e1^(r:0)*e2^(0:r))
  }

Hope this helps.

Petr Savicky.