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:
“The real weakness of England lies, not in incomplete armaments or unfortified coasts, not in the poverty that creeps through sunless lanes, or the drunkenness that brawls in loathsome courts, but simply in the fact that her ideals are emotional and not intellectual.”
—Oscar Wilde (1854–1900)
“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)
“Thoughts tending to content flatter themselves
That they are not the first of fortune’s slaves,
Nor shall not be the last, like silly beggars
Who, sitting in the stocks, refuge their shame
That many have and others must sit there,
And in this thought they find a kind of ease.”
—William Shakespeare (1564–1616)