Order of A Power Series
Let α be a multi-index for a power series f(x1, x2, …, xn). The order of the power series f is defined to be the least value |α| such that aα ≠ 0, or 0 if f ≡ 0. In particular, for a power series f(x) in a single variable x, the order of f is the smallest power of x with a nonzero coefficient. This definition readily extends to Laurent series.
Read more about this topic: Power Series
Famous quotes containing the words order of, order, power and/or series:
“There is no explanation for evil. It must be looked upon as a necessary part of the order of the universe. To ignore it is childish, to bewail it senseless.”
—W. Somerset Maugham (1874–1965)
“An honest man speaks the truth, though it may give offence; a vain man, in order that it may.”
—William Hazlitt (1778–1830)
“I had rather be shut up in a very modest cottage, with my books, my family and a few old friends, dining on simple bacon, and letting the world roll on as it liked, than to occupy the most splendid post which any human power can give.”
—Thomas Jefferson (1743–1826)
“History is nothing but a procession of false Absolutes, a series of temples raised to pretexts, a degradation of the mind before the Improbable.”
—E.M. Cioran (b. 1911)