Share 'wordpress.com and php'

I am working on a website for a non-profit group.   The current website is mostly static html & css, but we do have a php form (validates and stores data in small db and generates email notifications). Some folks in the group have suggested we move to wordpress.com.   But I don't see how I can add my php form on wordpress.com.  I understand how I could integrate the php form if I was running…