[R] Convergent series

[(Ted Harding)]

On 14-Jul-10 10:57:02, David Bickel wrote:
> What are some reliable R functions that can compute the value of a 
> convergent series?
> 
> David

Please give an example of a definition (as you would specify it
to an R function) of a "convergent series" that you want to compute!

Your query is about as general as could possibly be, and cannot
be presented to R as it stands, since a convergent series is an
infinite sequence of terms which could be anything so long as the
series converges.

There are already many R functions -- such as sin(), exp() -- which
compute values for specific convergent series, though often by
special methods which do not work through the series of terms.

Presumably a general series would be specified in terms of some
rule which defines the nth term in terms of the (n-1)th, and
possibly preceding, terms. Once such a specification has been
given, an R function can be written. Are you thinking of something
on the lines of

  sersum <- function(x,fun1,fun)

where fun1(x) would be a user-supplied function which computes
the first term as a function of x, and fun(x,n,tn) a user-supplied
function which computes term n in terms of tn=term (n-1), and n,
for n>1?

E.g. for the exponential series,

  fun1 <- function(x) 1
  fun  <- function(x,n,tn) tn*x/n

Ted.

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Date: 14-Jul-10                                       Time: 12:18:22
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