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A wavelet used for filtering signals. Daubechies (1988, p. 980) has tabulated the numerical values up to order p=10.

Delta_hf(x)=(f(x+h)-f(x))/h=(Deltaf)/h. It gives the slope of the secant line passing through f(x) and f(x+h). In the limit h->0, the difference quotient becomes the partial ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_n=f(x_n). Then Durand's rule approximating the ...

A Padé approximant perturbed with a Chebyshev polynomial of the first kind to reduce the leading coefficient in the error.

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

Let C_(L,M) be a Padé approximant. Then C_((L+1)/M)S_((L-1)/M)-C_(L/(M+1))S_(L/(M+1)) = C_(L/M)S_(L/M) (1) C_(L/(M+1))S_((L+1)/M)-C_((L+1)/M)S_(L/(M+1)) = ...

The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.

If x_1<x_2<...<x_n denote the zeros of p_n(x), there exist real numbers lambda_1,lambda_2,...,lambda_n such that ...

f(x) approx t_n(x)=sum_(k=0)^(2n)f_kzeta_k(x), where t_n(x) is a trigonometric polynomial of degree n such that t_n(x_k)=f_k for k=0, ..., 2n, and ...

The indefinite summation operator Delta^(-1) for discrete variables, is the equivalent of integration for continuous variables. If DeltaY(x)=y(x), then Delta^(-1)y(x)=Y(x).