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, power and/or series:
“The foot of the heavenly ladder, which we have got to mount in order to reach the higher regions, has to be fixed firmly in every-day life, so that everybody may be able to climb up it along with us. When people then find that they have got climbed up higher and higher into a marvelous, magical world, they will feel that that realm, too, belongs to their ordinary, every-day life, and is, merely, the wonderful and most glorious part thereof.”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)
“You cannot have power for good without having power for evil too. Even mother’s milk nourishes murderers as well as heroes.”
—George Bernard Shaw (1856–1950)
“As Cuvier could correctly describe a whole animal by the contemplation of a single bone, so the observer who has thoroughly understood one link in a series of incidents should be able to accurately state all the other ones, both before and after.”
—Sir Arthur Conan Doyle (1859–1930)