Trigonometric Polynomial - Formal Definition

Formal Definition

Any function T of the form

with a_n, b_n in C for 0 ≤ n ≤ N, is called a complex trigonometric polynomial of degree N (Rudin 1987, p. 88). Using Euler's formula the polynomial can be rewritten as

Analogously let a_n, b_n be in R, 0 ≤ n ≤ N and a_N ≠ 0 or b_N ≠ 0 then

is called real trigonometric polynomial of degree N (Powell 1981, p. 150).