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Re: Evaluating integral with varying upper limit?

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  • Subject: [mg71116] Re: Evaluating integral with varying upper limit?
  • From: "Jens-Peer Kuska" <kuska at>
  • Date: Thu, 9 Nov 2006 03:37:11 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <eimqg9$b9k$>


no because FunctionInterpolation[] construct a 
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}


"AES" <siegman at> schrieb im 
Newsbeitrag news:eimqg9$b9k$1 at
| Given a function  f[x]  which happens to be 
rather messy and not
| analytically integrable, I want to evaluate the 
|   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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