Formal power series
In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual algebraic operations on series (addition, subtraction, multiplication, division, partial sums, etc.). A formal power series is a special kind of formal series, of the form ∑ n = 0 ∞ a n x n = a 0 + a 1 x + a 2 x 2 + ⋯ , {\displaystyle \sum _{n=0}^{\infty }a_{n}x^{n}=a_{0}+a_{1}x+a_{2}x^{2}+\cdots ,} where the a n , {\displaystyle a_{n},} called coefficients, are numbers or, more generally, elements of some ring, and the x n {\displaystyle x^{n}} are formal powers of the symbol x {\displaystyle x} that is called an indeterminate or, commonly, a variable.