Re: [R] R: integration problem

From: Ravi Varadhan <rvaradha_at_jhsph.edu>
Date: Tue 11 Oct 2005 - 01:44:28 EST


Hi,

If your limits were to be from -1 to +1 (instead of lower limit being 0), your integral is:

pi * I_0(b)

Where I_0 is the modified Bessel's function of the zeroth order.

If it is from 0 to 1, then there is no closed form (the integrand is not symmetric about 0). You must evaluate the integral with exp(a*cos(t)) as the integrand from 0 to pi/2.

Hope this is helpful,
Ravi.

> -----Original Message-----
> From: r-help-bounces@stat.math.ethz.ch [mailto:r-help-
> bounces@stat.math.ethz.ch] On Behalf Of Clark Allan
> Sent: Monday, October 10, 2005 4:07 AM
> To: r-help@stat.math.ethz.ch
> Subject: [R] R: integration problem
>
> hi all
>
> an integration problem. i would like an exact or good approximation for
> the following, but i do not want to use a computer. any suggestions:
>
>
> integral of exp(b*x)/sqrt(1-x^2)
>
> where "b" is a constant greater than or equal to 0
> and
> the integral runs from 0 to 1
>
>
> any help would be apreciated
>
> /
> allan



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