MaplePrimes - answers and comments on Question, Getting MAPLE to generate output on indefinite integrals

I think the issue might lie with the cos(x) beneath the sq root

tsunamiBTP — Sun, 10 Jan 2010 01:53:24 Z

I was able to get MAPLE to generate an output if I had r^2-a^2*x within the sq root, but not cos(x). Why??

brackets

PatrickT — Sun, 10 Jan 2010 02:26:00 Z

the square brackets define a "list", replace them by round brackets.

[] -> ().

if problems arise, copy-paste your lines of code together with the error message (if any).

The brackets are not the problem but see my output

tsunamiBTP — Sun, 10 Jan 2010 03:55:00 Z

I used the brackets in this web browser editor, not in my MAPLE code. Nonetheless, I have attached my output. I attempted to transform the integral into a simpler form using variable substitutions. Eq. 1 shows the resulting transformation in terms of u. To solve this a number of integration by parts is likely required.

Can MAPLE not do this operation??? Note if I attempt to integrate with respect to phi MAPLE won't do the integral either.

http://www.mapleprimes.com/files/9288_integral output.pdf

integral output

Robert Israel — Sun, 10 Jan 2010 11:21:09 Z

The link should have been

www.mapleprimes.com/files/9288_integral output.pdf

(Maple Primes seems to have had trouble with the space in the file name).

The integral is

> int(exp(-I*k*sqrt(r^2-2*a*r*sin(theta)*cos(phi)+a^2)),phi=0..2*Pi);

My best guess is that there is no closed form for this. You could e.g. express the result as a series in powers of a:

> series(%,a) assuming r > 0;

series(2*exp(-I*k*r)*Pi+(-1/2*k*Pi*(I+k*r-k*r*cos(theta)^2+cos(theta)^2*I)*exp(-I*k*r)/r)*a^2+(-1/32*k*Pi*(-k^3*r^3*cos(theta)^4-2*I*k^2*r^2+15*k*r*cos(theta)^4+2*k^3*r^3*cos(theta)^2+I+6*I*cos(theta)^2-6*k*r*cos(theta)^2-4*I*k^2*r^2*cos(theta)^2+6*I*k^2*r^2*cos(theta)^4-15*I*cos(theta)^4-k^3*r^3-k*r)*exp(-I*k*r)/r^3)*a^4+O(a^6),a,6)