Final answer:
The Legendre polynomials are an orthogonal set of functions that are solutions to Legendre's equation. They have applications in solving boundary value problems and representing functions.
Step-by-step explanation:
The question is asking about the Legendre polynomial as an orthogonal set of functions. The Legendre polynomials are a set of solutions to a specific type of differential equation called Legendre's equation. These polynomials are orthogonal to each other, meaning that their inner product is zero when the polynomials have different indices. This property is important in various mathematical applications, such as solving boundary value problems and representing functions in a basis.