So the question is up and running here. It has two up votes and 20 views as of the time of writing (and 5 up votes and 51 views after some more time), and seems to be good!
Criterion that I requested for fulfillment from the new question, which were heeded, include :
The source, which was specified. It was found by the OP.
A reference to the old question.
A complete attempt for one part of the question, along with a partial attempt for the second part.
In addition, I have linked for the purposes of the OP and others' understanding, some posts above regarding the definition and some theorems about the HS function. These are here and here. The OP may feel free to use these documents to further the context of the question if necessary, or if prompted in the comments.
Either way, I thank the OP for their efforts to get the question running, and I hope it will receive an excellent answer and further improve the quality of the site, given that there hasn't been too much discussion on HS functions on the site.