A power series $${\textstyle \sum _{n=0}^{\infty }a_{n}(x-c)^{n}}$$ is convergent for some values of the variable x, which will always include x = c (as usual, $${\displaystyle (x-c)^{0}}$$ evaluates as 1 and … See more

In abstract algebra, one attempts to capture the essence of power series without being restricted to the fields of real and complex numbers, and without the need to talk about … See more

• Weisstein, Eric W. "Formal Power Series". MathWorld.
• Weisstein, Eric W. "Power Series". MathWorld. See more

Addition and subtraction
When two functions f and g are decomposed into power series around the same center c, the power series of the sum or difference … See more

A function f defined on some open subset U of R or C is called analytic if it is locally given by a convergent power series. This means that every a ∈ … See more

Let α be a multi-index for a power series f(x1, x2, …, xn). The order of the power series f is defined to be the least value $${\displaystyle r}$$ such … See more