Dear Søren,
An example that is more often used for this kind of thing is that of
fractional
powers of x on (0,1). These do not have a Maclaurin series due to the
infinite
derivatives at x=0.
Taking f=x^((2*n+1)/2), for n=0 both methods do quite poorly, needing
~10,000 points to achieve five place accuracy. For n=1, the integ1es takes
19 points while the trapz takes somewhere between 100 and 200. For n=2
through 5, it is 7 and some where between 500 and 1,000, respectively.
In the atan example of last corespondence, the trapz method was said to
be
prefered because it gave two digit accuracy with a smaller number of points
than did the integ1es. If such is the anticipated need, and it is not even
this
good for a number of frequently encountered distributions, then, indeed,
this
should be used.
Possable examples are endless, but I think the point has been
established.
The integ1es is quite general in its aplicability.
Expansions and corrections forthcoming.
Cheers,
dmelliott
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