Formal Definition
Any function T of the form
with an, bn 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 an, bn be in R, 0 ≤ n ≤ N and aN ≠ 0 or bN ≠ 0 then
is called real trigonometric polynomial of degree N (Powell 1981, p. 150).
Read more about this topic: Trigonometric Polynomial
Famous quotes containing the words formal and/or definition:
“The spiritual kinship between Lincoln and Whitman was founded upon their Americanism, their essential Westernism. Whitman had grown up without much formal education; Lincoln had scarcely any education. One had become the notable poet of the day; one the orator of the Gettsyburg Address. It was inevitable that Whitman as a poet should turn with a feeling of kinship to Lincoln, and even without any association or contact feel that Lincoln was his.”
—Edgar Lee Masters (1869–1950)
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)