Adding formulas/field calculations when creating custom fields via the manifest file.

Hey guys, 

I hope you are all well. I am currently work on a package to update our customer onboarding process. It would be preferred to install a single package in production and the configuration is complete except for adding the fields to the record layout.

In this process, I have check boxes on the Cases module an agent would check to create a related support setup ticket. Once this field is checked, there are other dependencies which become required, a text box should appear and be required. Normally I would just add the dependent formula in studio when creating the field, but when creating the fields with my manifest file, it is not clear how to add a dependent formula to a field.

Can anyone point me in the right direction?