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A set of functions {f_1(n,x),f_2(n,x)} is termed a complete biorthogonal system in the closed interval R if, they are biorthogonal, i.e., int_Rf_1(m,x)f_1(n,x)dx = ...

A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...

A plane curve of the form y=x^n. For n>0, the curve is a generalized parabola; for n<0 it is a generalized hyperbola.

Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function psi(x), sometimes ...

For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...

Let s(n)=sigma(n)-n, where sigma(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n)=n,s^1(n)=s(n),s^2(n)=s(s(n)),... ...

The terms of equational logic are built up from variables and constants using function symbols (or operations). Identities (equalities) of the form s=t, (1) where s and t are ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...

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 solution to a problem that can be written in "closed form" in terms of known functions, constants, etc., is often called an analytic solution. Note that this use of the ...