Flat polynomials and the POM

Let you forget, there was a Problem of the Month at the end of the term about Flat Polynomials.  The POM Guru has informed us at the OU Math Club blog that after settling a tie with an age old technique. The winner was

Karl Schaettle!

For those who are curious, the question was asking you to determine as many of the Chebyshev polynomials as you can.  They have lots of cool properties.  For example, if T_n(x) is the degree n Chebyshev polynomial, then the following integration formula is true:


The graph of the first few Chebyshev polynomials is below.