Statement
Consider a complex-valued, continuous function f, defined on a semicircular contour
of radius R > 0 lying in the upper half-plane, centred at the origin. If the function f is of the form
with a parameter a > 0, then Jordan's lemma states the following upper bound for the contour integral:
An analogous statement for a semicircular contour in the lower half-plane holds when a < 0.
Read more about this topic: Jordan's Lemma
Famous quotes containing the word statement:
“No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
—David Jenkins (b. 1925)
“He has the common feeling of his profession. He enjoys a statement twice as much if it appears in fine print, and anything that turns up in a footnote ... takes on the character of divine revelation.”
—Margaret Halsey (b. 1910)
“A sentence is made up of words, a statement is made in words.... Statements are made, words or sentences are used.”
—J.L. (John Langshaw)