The incomplete elliptic integral of the second kind E in trigonometric form is
Substituting, one obtains Jacobi's form:
Equivalently, in terms of the amplitude and modular angle:
Relations with the Jacobi elliptic functions include
The meridian arc length from the equator to latitude is written in terms of E:
where a is the semi-major axis, and e is the eccentricity.
Read more about this topic: Elliptic Integral
Famous quotes containing the words incomplete, integral and/or kind:
“Each of us is incomplete compared to someone else, an animal’s incomplete compared to a person ... and a person compared to God, who is complete only to be imaginary.”
—Georges Bataille (1897–1962)
“Self-centeredness is a natural outgrowth of one of the toddler’s major concerns: What is me and what is mine...? This is why most toddlers are incapable of sharing ... to a toddler, what’s his is what he can get his hands on.... When something is taken away from him, he feels as though a piece of him—an integral piece—is being torn from him.”
—Lawrence Balter (20th century)
“Fortunately, the time has long passed when people liked to regard the United States as some kind of melting pot, taking men and women from every part of the world and converting them into standardized, homogenized Americans. We are, I think, much more mature and wise today. Just as we welcome a world of diversity, so we glory in an America of diversity—an America all the richer for the many different and distinctive strands of which it is woven.”
—Hubert H. Humphrey (1911–1978)