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:
“Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.”
—Mario Vargas Llosa (b. 1936)
“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)
“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)