edit language (#213)

Author: onzerem

docs/src/index.md

@@ -17,16 +17,16 @@ 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:
+These special polynomials have many applications and can be used as a basis for any function given their domain conditions are met, however these polynomials have some advantages due to their formulation:
 
-- **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.
+- Because of their relation to Laplace’s equation, **Legendre polynomials** can be useful as a basis for functions with spherical symmetry.
+- **Chebyshev polynomials** are generally effective in reducing errors from numerical methods such as quadrature, interpolation, and approximation.
+- Due to the flexibility of its parameters, **Jacobi polynomials** are capable of tailoring the behavior of an approximation around its endpoints, making these polynomials particularly useful in boundary value problems.
+- **Ultraspherical polynomials** are advantageous in spectral methods for solving differential equations.
+- **Laguerre polynomials** have a semi-infinite domain, therefore they are beneficial for problems involving exponential decay.
+- Because of its weight function, **Hermite polynomials** can be useful in situations where functions display a Gaussian-like distribution.
 
-These are just a few key applications of these polynomials. They have many more uses across mathematics, physics, and engineering.
+These are just a few applications of these polynomials. They have many more uses across mathematics, physics, and engineering.
 
 ## Evaluation