Converting matlab to C - matrix operator

Hi I am trying to convert the following lines of code into C, but I am not completely sure what the matlab operator is actually doing here:

x = (exp(a*2*pi)-cosh(a*b*T0))./sinh(a*b*T0);
c1 = b^2*(x.^2-1);
f = sum(abs(c1.*exp(-2*a*theta_f)+nu*((1+0.5*(4*a^2+1))*cos(theta_f+phi)-2*a*sin(theta_f+phi))+b^2-wf2));

T0 is a column vector 23 long. So I think on the x line, matlab is just doing the calculation using every value of T0 and producing 23 values for x - one for each T0. c1 line is the then producing a vector c1 also 23 long from the vector x. Then f is also producing 23 values, however it takes the absolute then sums them? is this correct? because it also produces a number if i take all the '.' out