If there is a wider question based on the 'submission of the thesis given a problem' aspect, it might be worth asking/checking on the Academia StackExchange. You've already done the work, so having to redo anything major is probably out of scope at this point (funding, time, ... etc.), and that shouldn't prevent you from submitting or getting the PhD. It's just a matter of clearly stating any assumptions made and the limitations surrounding the work, and preparing for the viva with this in mind. Don't fall into the trap of having the PhD drag on forever to make it 'perfect'.

Also looks like it will have something to do with Bernoulli polynomials.