Similarly, see Pavel Grinfeld's argument [2] advocating the vector basis L = {1, x, x²-1/3} w.r.t. Legendre polynomials.

[1] https://en.wikipedia.org/wiki/Pavel_Grinfeld

[2] MathTheBeautiful: Why {1,x,x²} Is a Terrible Basis [video] https://www.youtube.com/watch?v=pYoGYQOXqTk&index=14&list=PL....

[3] https://en.wikipedia.org/wiki/Legendre_polynomials