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In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
Plot of the Whittaker function M k,m(z) with k=2 and m= 1 / 2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by Whittaker () to make the formulas involving the solutions more ...
The Mandelbrot set, one of the most famous examples of mathematical visualization. Mathematical phenomena can be understood and explored via visualization . Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).
List of mathematical functions; List of mathematical identities; List of mathematical proofs; List of misnamed theorems; List of scientific laws; List of theories; Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields.
One possible proof outline is as follows. If is finite, it suffices to take () = ().If is not finite, consider the finite sum () = where is a finite subset of .While the () may not converge as F approaches E, one may subtract well-chosen rational functions with poles outside of (provided by Runge's theorem) without changing the principal parts of the () and in such a way that convergence is ...
Many special functions appear as solutions of differential equations or integrals of elementary functions.Therefore, tables of integrals [1] usually include descriptions of special functions, and tables of special functions [2] include most important integrals; at least, the integral representation of special functions.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.