Power Series - Order of A Power Series

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:

    Life does not need to mutilate itself in order to be pure.
    Simone Weil (1909–1943)

    The terror of the atom age is not the violence of the new power but the speed of man’s adjustment to it—the speed of his acceptance.
    —E.B. (Elwyn Brooks)

    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)