Recent content by Fraggler

Thanks for your reply Villyer. I've just solved it, with some help from a friend. Here's the solution. For x \approx 0 , (\frac{1 - x}{x})^k = x^{-k} . Therefore, f(p) = \int_0^p x^{-k} dx = \frac{1}{1-k} p^{1 - k} , as required. Cheers!

This problem arises in a paper on population genetics (Kimura 1962). 1. The problem statement Let f(p) = \int_0^p ((1 - x)/x)^k dx. For a small value of p, we have approximately f(p) = (p ^ (1-k)) / (1-k) How is this obtained? 2. My attempt at a solution I tried to expand the f(p) around p =...

What Lagrangian would you set up? We want to find the path that minimizes W = integral F dot dr. How do you solve for a path? I apologize for the sloppy notation; this is my first post and I'm not familiar with tricks to get the integral and dot product signs to show up.