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One of the main results of the theory of elliptic functions is the following: Every elliptic function with respect to a given period lattice can be expressed as a rational function in terms of ℘ and ℘ ′. [7] The ℘-function satisfies the differential equation
The fundamental rectangle in the complex plane of . There are twelve Jacobi elliptic functions denoted by (,), where and are any of the letters , , , and . (Functions of the form (,) are trivially set to unity for notational completeness.) is the argument, and is the parameter, both of which may be complex.
In mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass . This class of functions is also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p .
In mathematics, specifically the theory of elliptic functions, the nome is a special function that belongs to the non-elementary functions. This function is of great importance in the description of the elliptic functions, especially in the description of the modular identity of the Jacobi theta function, the Hermite elliptic transcendents and the Weber modular functions, that are used for ...
Fundamenta nova theoriae functionum ellipticarum [1] (from Latin: New Foundations of the Theory of Elliptic Functions) is a treatise on elliptic functions by German mathematician Carl Gustav Jacob Jacobi. [2] The book was first published in 1829, and has been reprinted in volume 1 of his collected works and on several later occasions.
One of Jacobi's greatest accomplishments was his theory of elliptic functions and their relation to the elliptic theta function.This was developed in his great treatise Fundamenta nova theoriae functionum ellipticarum (1829), and in later papers in Crelle's Journal.
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O.An elliptic curve is defined over a field K and describes points in K 2, the Cartesian product of K with itself.
Pages in category "Elliptic functions" The following 31 pages are in this category, out of 31 total. This list may not reflect recent changes. ...