What is difference between Taylor series and Legendre polynomial?

1. Are Taylor series and polynomials the same?
2. What is the difference between Legendre function and Legendre polynomial?
3. What do you mean by Legendre polynomial?
4. What is the Taylor series of a polynomial?

Are Taylor series and polynomials the same?

The difference between a Taylor polynomial and a Taylor series is the former is a polynomial, containing only a finite number of terms, whereas the latter is a series, a summation of an infinite set of terms, any number of which (including an infinite number) may be zero.

What is the difference between Legendre function and Legendre polynomial?

. A two-parameter generalization of (Eq. 1) is called Legendre's general differential equation, solved by the Associated Legendre polynomials. Legendre functions are solutions of Legendre's differential equation (generalized or not) with non-integer parameters.

What do you mean by Legendre polynomial?

To get the polynomial solution when k is even, take a₁ = 0 and a₀ ≠ 0. The solution is. To get the polynomial solution when k is odd, take a₀ = 0 and a₁ ≠ 0. The solution is. In these cases, the solution is called the Legendre polynomial of degree k.

What is the Taylor series of a polynomial?

A Taylor series is a clever way to approximate any function as a polynomial with an infinite number of terms. Each term of the Taylor polynomial comes from the function's derivatives at a single point.