The quotes are intentional. Without them you have create a local lambda function and are passing that to the TF1 constructor. Hence you are using a different constructor to the one I am using.
I am specifically using the one I am as I need the TF1 to be self contained, and not rely on an external lambda function to operator. If you where to return your function from a method (which I do) then your function will be ill defined once the scope of the method is closed, as then the lambda will no longer exist. In my case it does.
See
https://root.cern.ch/doc/master/classTF1.html
case 3.