Hi Mahmudul,
I'm looking at the summation term in the denominator. It says to take the difference of vectors x and y, and then the absolute value ... which I believe you mean element-wise(?), and then sum element-wise(?). If so, then we're good so far.
Then I gather you'd like a finite or infinite series expansion of the rational expression. Sure, that's doable and there are many types of expansions to consider. Did you have any particular one in mind?