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

Which of the following is holds true for the Chebyshev polynomial?(a)

1.	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» The correct OPTION is (a) TM(-x) = (-1)^m Tm(x) The best EXPLANATION: The Chebyshev polynomial is given by T0(x)=1m=0 T1(x)=xm=1 T2(x)=2x^2-1m=2 T3(x)=4x^3-3xm=3 There fore Tm(-x)=(-1)^m Tm (x) holds true.

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