Dimensional regularization : we integrate over all of R d , but instead of considering d to be a positive integer, we analytically continue d to d = n − − ϵ ϵ , where ϵ ϵ is small. By the computation above, we showed that the integral can be written in terms of expressions which have a well-defined analytic continuation from integers n to functions on C : specifically the gamma function has an analytic continuation and taking powers, x d , is an operation which can be analytically continued.