R help - Oct 2005 - 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

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