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)
“Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.”
—Charles Sanders Peirce (1839–1914)
“The parent is the strongest statement that the child hears regarding what it means to be alive and real. More than what we say or do, the way we are expresses what we think it means to be alive. So the articulate parent is less a telling than a listening individual.”
—Polly Berrien Berends (20th century)