In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance. Many of their features show up in important structures and have direct relevance to some applications (e.g. the equation of a pendulum—also see pendulum (mathematics)). They also have useful analogies to the functions of trigonometry, as indicated by the matching notation sn for sin. The Jacobi elliptic functions occur more often in practical problems than the Weierstrass elliptic functions. They were introduced by Carl Gustav Jakob Jacobi (1829).
Read more about Jacobi Elliptic Functions: Introduction, Notation, Definition As Inverses of Elliptic Integrals, Definition in Terms of Theta Functions, Minor Functions, Addition Theorems, Relations Between Squares of The Functions, Expansion in Terms of The Nome, Jacobi Elliptic Functions As Solutions of Nonlinear Ordinary Differential Equations, Map Projection
Famous quotes containing the words jacobi and/or functions:
“During the long ages of class rule, which are just beginning to cease, only one form of sovereignty has been assigned to all menthat, namely, over all women. Upon these feeble and inferior companions all men were permitted to avenge the indignities they suffered from so many men to whom they were forced to submit.”
—Mary Putnam Jacobi (18421906)
“Nobody is so constituted as to be able to live everywhere and anywhere; and he who has great duties to perform, which lay claim to all his strength, has, in this respect, a very limited choice. The influence of climate upon the bodily functions ... extends so far, that a blunder in the choice of locality and climate is able not only to alienate a man from his actual duty, but also to withhold it from him altogether, so that he never even comes face to face with it.”
—Friedrich Nietzsche (18441900)