Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications. There is no general formal definition, but the list of mathematical functions contains functions which are commonly accepted as special. In particular, elementary functions are also considered as special functions.
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Sinc function
In mathematics and engineering, the sinc function, denoted by sinc(x), has two slightly different definitions. In mathematics, the historical unnormalized sinc function is defined by In digital signal processing and information theory, the normalized sinc function is commonly defined by It is qualified as normalized because its integral over all x is 1. All of the zeros of the normalized sinc function are integer values of x.
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MATLAB
MATLAB (matrix laboratory) is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran.
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Initial value problem
In mathematics, in the field of differential equations, an initial value problem (also called the Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them.
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Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines.
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Collocation method
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-dimensional space of candidate solutions (usually, polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the given equation at the collocation points.
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Laguerre polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 – 1886), are solutions of Laguerre's equation: which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer.
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