From: Ravi Varadhan <rvaradha_at_jhsph.edu>

Date: Tue 11 Oct 2005 - 01:44:28 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Oct 11 01:59:52 2005

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
*

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Oct 11 01:59:52 2005

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