       Re: Evaluating integral with varying upper limit?

• To: mathgroup at smc.vnet.net
• Subject: [mg71116] Re: Evaluating integral with varying upper limit?
• From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
• Date: Thu, 9 Nov 2006 03:37:11 -0500 (EST)
• Organization: Uni Leipzig
• 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 . . .
|

```

• Prev by Date: [Help Needed] Converting C++ program into Mathematica Function
• Next by Date: Re: Question about trig simplify
• Previous by thread: Re: Evaluating integral with varying upper limit?
• Next by thread: Help needed