by George F. Schils
Years ago around the time of 1975-1976, I wanted to investigate some polynomial curve fitting. Being very excited by polynomial techniques and having just "gotten started" learning about special functions, I decided to try out some curve fitting using Legendre polynomial techniques. I chose the function Sqrt(x) and decided to try to find the "best" fourth order polynomial that would fit this function in the sense of minimum integrated squared error.
I worked through a solution using a hand calculator (HP 35 I think) and paper. Many details are left out, and the solution obtained is presented below.
This was an interesting exercise. I have always found Legendre polynomials to be interesting, and I still find them to be interesting.
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