User blog comment:Naruyoko/My Utterly Obscure and Slowly Evolve-Growing Function-Notation-Whatever/@comment-27516045-20190218205725

Let's see here...

 = 2a+2

 =  = 2a+3

 =  =  = 2a+b+2

 =  = 3a+2

 =  = 4a+2

 = (a+1)*a+2 = a^2+a+2

 = a^2+2a+2

Your function's limit growth rate in SGH is w^2+w2+2! Nice job!