Apr 01, 2016 08:05 AM|Weibo Zhang|LINK
According to your above description, I think you want to download a PDF file through the ajax and web service. The following link provides a demo about using Iframe to achieve it that you could have a look.
In link provides a demo about first build the contents of PDF through ajax calling web service during page loading and then use Server button to download the PDF, maybe you could have a look.
Besides, the following article shows a demo about using Ajax and a generic handler to do it and you could have a try if you need.