Question

Which of the following is holds true for the Chebyshev polynomial?

(a) Tm(-x) = (-1)^m Tm(x)

(b) Tm(-x) = (-1)^m Tm-1(1/x)

(c) Tm(x) = (-1)^m Tm(1/x)

(d) Tm(-x) = (-1)^m Tm-1(x)

This question was posed to me during a job interview.

My enquiry is from Adaptive Array topic in portion Phased, Adaptive and Binomial Arrays of Antennas

Answer 1

The correct option is (a) Tm(-x) = (-1)^m Tm(x)

The best explanation: The Chebyshev polynomial is given by

T0(x)=1             m=0

T1(x)=x             m=1

T2(x)=2x^2-1   m=2

T3(x)=4x^3-3x  m=3

There fore Tm(-x)=(-1)^m Tm (x) holds true.