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:
“All the sciences are now under an obligation to prepare for the future task of philosopher, which is to solve the problem of value, to determine the rank order of values.”
—Friedrich Nietzsche (1844–1900)
“In Europe, charters of liberty have been granted by Power. In America ... charters of power [are] granted by liberty.”
—James Madison (1751–1836)
“There is in every either-or a certain naivete which may well befit the evaluator, but ill- becomes the thinker, for whom opposites dissolve in series of transitions.”
—Robert Musil (1880–1942)