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The Cesàro means of a function f are the arithmetic means sigma_n=1/n(s_0+...+s_(n-1)), (1) n=1, 2, ..., where the addend s_k is the kth partial sum ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

A substitution which can be used to transform integrals involving square roots into a more tractable form. form substitution sqrt(x^2+a^2) x=asinhu sqrt(x^2-a^2) x=acoshu

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

The crossed trough is the surface z=x^2y^2. (1) The coefficients of its first fundamental form are E = 1+4x^2y^4 (2) F = 4x^3y^3 (3) G = 1+4x^4y^2 (4) and of the second ...

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 = ...

There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

Expresses a function in terms of its Radon transform, f(x,y) = R^(-1)(Rf)(x,y) (1) = ...

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...