Some characterizations of Pearson's Two-Unequal Step Random

More than a century ago, Pearson (1905) proposed the following: A man starts from a point $0$ and walks $\ell$ yards in a straight line, then he turns any angle whatever and walks $\ell$ yards in a straight line. He repeats this process $n$ times. I require the probability that after $n$ steps he is at a distance $r$ and $r + dr$ from the starting point $0$. In this paper some characterizations of the the random walk of unequal step size are given.