Search results
Results from the WOW.Com Content Network
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...
The name Desmos came from the Greek word δεσμός which means a bond or a tie. [6] In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7]
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.
Bessel functions describe the radial part of vibrations of a circular membrane.. Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation + + = for an arbitrary complex number, which represents the order of the Bessel function.
In those days the theory of elliptic functions and the theory of doubly periodic functions were considered to be different theories. They were brought together by Briot and Bouquet in 1856. [20] Gauss discovered many of the properties of elliptic functions 30 years earlier but never published anything on the subject. [21]
The lemniscate functions sl and cl can be defined as the solution to the initial value problem: [5] = (+ ) , = (+ ) , =, =, or equivalently as the inverses of an elliptic integral, the Schwarz–Christoffel map from the complex unit disk to a square with corners {,,,}: [6]
The Dixon elliptic functions cm, sm applied to a real-valued argument x.Both functions are periodic with real period π 3 ≈ 5.29991625. In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in a hexagonal tiling to the whole complex plane.
If () is a general scalar-valued function of a normal vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can be computed with the numerical method of ray-tracing (Matlab code). [17]