Definition
Formally, an elliptic function is a function meromorphic on for which there exist two non-zero complex numbers and with (in other words, not parallel), such that and for all .
Denoting the "lattice of periods" by, it follows that for all .
There are two families of 'canonical' elliptic functions: those of Jacobi and those of Weierstrass. Although Jacobi's elliptic functions are older and more directly relevant to applications, modern authors mostly follow Karl Weierstrass when presenting the elementary theory, because his functions are simpler, and any elliptic function can be expressed in terms of them.
Read more about this topic: Elliptic Function
Famous quotes containing the word definition:
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)