Symbolic inverse fourier transform help, ifourier

I have a symbolic function I am trying to take the Inverse Fourier Transform of, using ifourier.

Here is the function

f = exp((x*(13275529002761960*x^2 + x*(3719000583476212*i) - 5780029644482843)*i)/281474976710656)

Then I take the Inverse Fourier by

inverse_f = ifourier(f, x, t);

and I get the following answer

inverse_f = fourier(exp((x*(13275529002761960*x^2 + x*(3719000583476212*i) - 5780029644482843)*i)/281474976710656), x, -t)/(2*pi)

I don't see what I am doing wrong. Can ifourier not handle more complicated functions? Is there another way of transforming this?

Thank you.

[Star Strider]

What is:

firstchar_cum

?

[Salvatore]

Sorry, it should read

inverse_f = ifourier(f, x, t);

I fixed it in the above question.

[Anurag Agarwal]

Salvator, were you able to find the solution for this? If yes, please share.

[David Goodmanson]

Hello Salvatore,

The only thing you may be doing wrong is expecting to find an analytic solution for this integral (including the exp(2*pi*i*x*t) part). The exponent contains a cubic polynomial in x. It might just be doable if you use a change of variable to eliminate the x^2 term and get a*x^3 + b*x + c, as is the standard first step when solving a cubic. Then with enough work you might be able to reduce the answer to various sums of bessel functions of order +-1/3. See the definition of the Airy function in terms of integrals.