add to doc: choosing poly (JuliaApproximation#213)

docs/src/index.md

@@ -17,6 +17,17 @@ which defines the following classical orthogonal polynomials:
 5. Laguerre: `L_n^{(α)}(x)`
 6. Hermite: `H_n(x)`
 
+Each of these polynomials has unique advantages and applications:
+
+- **Legendre polynomials** are suited to problems involving spherical coordinates.
+- **Chebyshev polynomials** are effective in reducing errors from numerical methods such as quadrature, interpolation, and approximation.
+- **Ultraspherical polynomials** are an extension of Legendre and Chebyshev polynomials. They are useful for spherical harmonics in higher dimensions. 
+- **Jacobi polynomials** are useful in tailoring polynomial behavior over specific intervals, especially around boundary points. 
+- **Laguerre polynomials** are suited to problems involving exponential growth and decay due to their semi-infinite domain.
+- **Hermite polynomials** are used in fields involving Gaussian distributions such as quantum mechanics, probability analysis, and signal processing.
+
+These are just a few key applications of these polynomials. They have many more uses across mathematics, physics, and engineering.
+
 ## Evaluation
 
 The simplest usage of this package is to evaluate classical