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MathGroup Archive 2006

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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 . . .
| 



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