Question

The recurrence relation for the Chebyshev polynomial is __________

(a) Tm(z) = 2zTm-1(z) – Tm-2(z)

(b) Tm (z) = Tm-1(z) – 2zTm-2(z)

(c) Tm(z) = 2zTm(z) – Tm-2(z)

(d) Tm(z) = 2zTm(z) – Tm-1(z)

I had been asked this question in unit test.

I'd like to ask this question from Adaptive Array in division Phased, Adaptive and Binomial Arrays of Antennas

Answer 1

Right answer is (a) Tm(z) = 2zTm-1(z) – Tm-2(z)

Explanation: The Chebyshev polynomial of any order m can be derived from the recursive formula. This is one of the main features of the Chebyshev polynomial. The recurrence relation for the Chebyshev polynomial is

Tm(z) = 2zTm-1(z) – Tm-2(z).