Complex Integrals
For complex integrals in the form:
with t >> 1, we make the substitution t = iu and the change of variable s = c + ix to get the Laplace bilateral transform:
We then split g(c+ix) in its real and complex part, after which we recover u = t / i. This is useful for inverse Laplace transforms, the Perron formula and complex integration.
Read more about this topic: Laplace's Method
Famous quotes containing the word complex:
“The human mind is so complex and things are so tangled up with each other that, to explain a blade of straw, one would have to take to pieces an entire universe.... A definition is a sack of flour compressed into a thimble.”
—Rémy De Gourmont (1858–1915)