Inverse Fourier Transform help (pdf from first characteristic function)

Hello,

I have a program that generates a truncated version of the second characteristic function (cumulant generating function) of a random variable. From this I calculate first characteristic function (moment generating function), using the following loop:

syms s x  
firstchar = 1;
for i = 1:k
    firstchar = firstchar*exp(s^(i)*cumulant(i)/factorial(i));
end

Next I take the inverse Fourier Transform of the first characteristic function to get the pdf. This is all done symbolically with the following code

f_cs = simplify(eval(firstchar));
f_cs = subs(f_cs, s, -1i*x);
pdf = ifourier(f_cs, x, t);

In most cases (for i > 2 in the above loop) I am not able to find a closed form of the pdf.

Can anyone help? I don't necessarily need to do this symbolically, and have tried using ifft, but nothing seems to work. Any ideas?

Thank you.