Direct determination of the coefficients of Chebyshev polynomials and other considerations

A closed-form expression to obtain the coefficients of a Chebyshev polynomial is presented. This result allows direct determination of the coefficients of Chebyshev polynomials without requiring further algebraic manipulations or using recursion formulas. For even order, a closed formula is given when the Chebyshev polynomial is modified in such a way that the resulting even order low pass magnitude characteristic has a passive ladder realization with equal terminating resistances