Re: Evaluating integral with varying upper limit?
- To: mathgroup at smc.vnet.net
- Subject: [mg71113] Re: Evaluating integral with varying upper limit?
- From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
- Date: Wed, 8 Nov 2006 06:16:53 -0500 (EST)
- References: <eimqg9$b9k$1@smc.vnet.net>
Hi,
no because FunctionInterpolation[] construct a
InterpolatingFunction[]
that is a piecewise polynomial and polynoms will
never have
"finite limiting value as y -> Infinity?"
You can try NumericalMath`Approximations` and
construct a rational
approximation and keep your fingers crossed that
the rational
approximation has no singularity inside the
interval {ymin,Infinity}
Regards
Jens
"AES" <siegman at stanford.edu> schrieb im
Newsbeitrag news:eimqg9$b9k$1 at smc.vnet.net...
| Given a function f[x] which happens to be
rather messy and not
| analytically integrable, I want to evaluate the
function
|
| g[y_] := NIntegrate[f[x], {x, ymin, y} ]
|
| with ymin fixed and ymin < y < Infinity.
|
| I suppose that FunctionInterpolate is the way to
go here (???).
|
| But, are there tricks to tell
FunctionInterpolate what I know in
| advance, namely that f[x] is everywhere
positive, and decreases toward
| zero rapidly enough at large x that g[y] will
approach a finite limiting
| value as y -> Infinity? (which value I'd like to
have FI obtain with
| moderate accuracy -- meaning 3 or 4 significant
digits, not 10 or 20)
|
| Thanks . . .
|