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:
““New order of the ages” did we say?
If it looks none too orderly today,
‘Tis a confusion it was ours to start
So in it have to take courageous part.”
—Robert Frost (1874–1963)
“I write poetry in order to live more fully.”
—Judith Rodriguez (b. 1936)
“Being a parent is a form of leadership. . . . Parents make a mistake, along with leaders of organizations, when they are unwilling to recognize the power inherent in the positions they occupy and when they are unwilling to use this power. . . . I do not mean a figure who is irrational, autocratic, or sadistic. I mean leaders who have the strength of character to stand up for what they believe.”
—Abraham Zaleznik. In Support of Families, ed. Michael W. Yogman and T. Berry Brazelton, ch. 8 (1986)
“In the order of literature, as in others, there is no act that is not the coronation of an infinite series of causes and the source of an infinite series of effects.”
—Jorge Luis Borges (1899–1986)