I have a function that does not necessarily have an analytical solution, but I have been able to solve it numerically using Mathematica. But, I am only interested in a section of the function to study (its average, rms and minimum). Here is my problem in more detail:
Given the gaussian function:
I am interested evaluating the following function:
Where now I have f as a function of y. Using Mathematica I am able to numerically solve for f(y) and plot the function which is shown below:
Now, my issue is that I am ONLY interested in describing the negative 'dip' of f(y) (peaking t approximately y=0) and not at all interested in the positive peak in the +y direction.
So, I was wondering if there is any analytical manipulations I could do to lambda or f(y) to isolate and describe the negative 'dip' results?
Thanks for any help in advance!