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The thin plate spline is the two-dimensional analog of the cubic spline in one dimension. It is the fundamental solution to the biharmonic equation, and has the form ...

Rather surprisingly, trigonometric functions of npi/17 for n an integer can be expressed in terms of sums, products, and finite root extractions because 17 is a Fermat prime. ...

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation w=f(z) that preserves ...

The Jack polynomials are a family of multivariate orthogonal polynomials dependent on a positive parameter alpha. Orthogonality of the Jack polynomials is proved in Macdonald ...

Operations research is a vast branch of mathematics which encompasses many diverse areas of minimization and optimization. Thousands of books have been written worldwide on ...

A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

Pre-Calculus