Formal power series
Operations
Multiplication
Multiplying two finite formal power series is the same as multiplying two polynomials. That can be done in $O(n\log n)$ time with Fast Fourier transform
Division
Calculating the multiplicative inverse of a formal power series can be done in $O(n\log n)$. 1
Square root
Calculating the square root of a formal power series can be done in $O(n\log n)$. 1