Hi, Hi, I have started to work with the R2009b version of the symbolic toolbox. I would like to have some help with integration. Consider the following code : syms x m p f=exp(-m/x^2-p*x^2) integ=int(f,0,inf) taylor(f,6)
I get a message that an explicit integral cannot be found. Fair enough. Except that I know that the answer is : sqrt(pi)/2/sqrt(p)*exp(-2*sqrt(m*p)) Even though I know the answer, I want to use the symbolic toolbox for more complicated forms of the above integral. To do this, I went in the opposite direction by starting with even simpler forms of the integral. For example : int(exp(-p*x^2),0,inf) For which, I should get the answer : 1/2*sqrt(pi/p) Instead, I got the following message : warning: Explicit integral could not be found.
piecewise([p < 0, Inf], [(0 <= Re(p) or abs(arg(p)) <= pi/2) and p <> 0, pi^(1/2)/(2*p^(1/2))], [Otherwise, int(1/exp(x^2*p), x = 0..Inf)]) Is there some way of proceeding here, that I am missing?
Finally, I tried to get taylor series expansion >> taylor(exp(-m/x^2-p*x^2),6) Warning: cannot compute a Taylor expansion of exp(- m/x^2 - p*x^2). Try 'series' with one of the options 'Left', 'Right', or 'Real' for a more general expansion [taylor]
taylor(1/exp(m/x^2 + p*x^2), x = 0, 6, AbsoluteOrder)
How do I interpret this? Should I use "series" somehow in the taylor function? The syntax for the taylor command does not seem to allow any such a possibility.
Any and all help will be appreciated. As you can see, I am just beginning to get acquainted with the symbolic toolbox. Thanks, Ravi