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

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