Examples of second solutions to differential equations for Legendre and Chebyshev polynomials, contrasting behavior in x and n.
Explains the term 'ultraspherical' in mathematics, clarifying why Gegenbauer polynomials are called ultraspherical and their connection to hyperspheres.
Compares the accuracy and behavior of Fourier, Legendre, and Taylor series expansions when approximating functions with a limited number of terms.
Explores generalized Fourier series expansions using orthogonal function bases, with examples from Legendre polynomials and practical Jupyter notebook code.
