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 . . . |