1.14. Dimensional regularization Let d the dimension of the space. Discuss the convergence of the integral I

(d) = 

∞

0 rd−1 r2 +1 dr by varying d.

a. Determine, in its convergent domain, the exact expression of the integral as a function of d and identify the position of its poles.

b. Analytically continue the definition of the integral in any other domain.

c. Compute its value for d = 13 and d = π.

Hint:Consider the integral in the complex plane 
C zd−1 z2 +1 dz where C is the contour shown in Figure 1.10.