Search Results for ""

The Abel-Plana formula gives an expression for the difference between a discrete sum and the corresponding integral. The formula can be derived from the argument principle ...

The discrete Fourier transform of length N (where N is even) can be rewritten as the sum of two discrete Fourier transforms, each of length N/2. One is formed from the ...

A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

A number x in which the first n decimal digits of the fractional part frac(x) sum to 666 is known as an evil number (Pegg and Lomont 2004). However, the term "evil" is also ...

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

A generalization of the hypergeometric function identity (1) to the generalized hypergeometric function _3F_2(a,b,c;d,e;x). Darling's products are (2) and (3) which reduce to ...

The Fourier transform of the constant function f(x)=1 is given by F_x[1](k) = int_(-infty)^inftye^(-2piikx)dx (1) = delta(k), (2) according to the definition of the delta ...