Search results
Results from the WOW.Com Content Network
Representing Functions as Power Series. Being able to represent a function by an “infinite polynomial” is a powerful tool. Polynomial functions are the easiest functions to analyze, since they only involve the basic arithmetic operations of addition, subtraction, multiplication, and division.
Use a power series to represent a function. Being able to represent a function by an “infinite polynomial” is a powerful tool. Polynomial functions are the easiest functions to analyze, since they only involve the basic arithmetic operations of addition, subtraction, multiplication, and division.
To use the Geometric Series formula, the function must be able to be put into a specific form, which is often impossible. However, use of this formula does quickly illustrate how functions can be represented as a power series. We also discuss differentiation and integration of power series.
Representing Functions as Power Series. Being able to represent a function by an "infinite polynomial" is a powerful tool. Polynomial functions are the most manageable functions to analyze since they only involve the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now we know that some functions can be expressed as power series, which look like infinite polynomials. Since calculus, that is, computation of derivatives and antiderivatives, is easy for polynomials, the obvious question is whether the same is true for infinite series.
Functions as Power Series. A power series ∑n=0∞ cnxn ∑ n = 0 ∞ c n x n can be thought of as a function of x x whose domain is the interval of convergence. Conversely, m any functions can be expressed as power series, and we will be learning various ways to do this.
we can represent these new functions using power series, we can then use substitution and term–by–term differentiation and integration to obtain power series for functions related to them. The following table collects some of the power series representations we have obtained in this section.
Representing Functions as Power Series. Being able to represent a function by an “infinite polynomial” is a powerful tool. Polynomial functions are the easiest functions to analyze, since they only involve the basic arithmetic operations of addition, subtraction, multiplication, and division.
First, we examine how to use the power series representation of the function g(x) = 1=(1 interval ( 1; 1) to derive a power series representation of other functions on an interval. Example (Substitution) Find a power series representation of the functions given below and interval of convergence of the series.
Representing Functions as Power Series. Derivatives and Integrals of Power Series. As long as we are strictly inside the interval of convergence, we can take derivatives and integrals of power series allowing us to get new series.