1. The problem statement, all variables and given/known data p(t) = integral[-inf,+inf] ( x/sinh(x) exp (i t x) dx) 2. Relevant equations singularity @ x = n*pi*i where n = +-1, +-2, +-3,... Near n*pi*i one can write sinh(x) ~ (x - n*pi*i) 3. The attempt at a solution I apply the cauchy residue theorem. For a positive value of t the contour of integrat can be closed with a semicircle in a positive complex x plane. Hence, p = (2*pi*i) * SUM ( n*pi*i) (-1)^n exp(-n*pi*t) ???? p = pi^2/ ( 1 + cosh( pi*t) ) ???? According to the reference i have, the answer should have been p = pi / (4*cosh^2(pi*t/2) ) I would really appreciate your help in this matter. More power.