It seems to me that your double integrals do not parse correctly. Repeatedly click inside your formulas and see how the terms group together. You had better enter the double integrals again using the unambiguous ascii syntax
Integrate[
Integrate[function, {\[Xi], 0, Infinity}], {s, (-I) Infinity,
I*Infinity}]
and avoid the traditional integral notation when typing the input, because it can be interpreted the wrong way.
