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: integration problem
3 messages · Clark Allan, Uwe Ligges, Ravi Varadhan
Clark Allan wrote:
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)
Sounds like the problem of integrating the Gaussian density... Uwe Ligges
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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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 at stat.math.ethz.ch [mailto:r-help- bounces at stat.math.ethz.ch] On Behalf Of Clark Allan Sent: Monday, October 10, 2005 4:07 AM To: r-help at 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