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A matrix H with elements H_(ij)=(i+j-1)^(-1) (1) for i,j=1, 2, ..., n. Hilbert matrices are implemented in the Wolfram Language by HilbertMatrix[m, n]. The figure above shows ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...

The Hilbert transform (and its inverse) are the integral transform g(y) = H[f(x)]=1/piPVint_(-infty)^infty(f(x)dx)/(x-y) (1) f(x) = ...

The 21 assumptions which underlie the geometry published in Hilbert's classic text Grundlagen der Geometrie. The eight incidence axioms concern collinearity and intersection ...

A determinant which arises in the solution of the second-order ordinary differential equation x^2(d^2psi)/(dx^2)+x(dpsi)/(dx)+(1/4h^2x^2+1/2h^2-b+(h^2)/(4x^2))psi=0. (1) ...

The second-order ordinary differential equation (d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0, (1) where theta_n are fixed constants. A general solution can be ...

Let ad=bc, then Hirschhorn's 3-7-5 identity, inspired by the Ramanujan 6-10-8 identity, is given by (1) Another version of this identity can be given using linear forms. Let ...

The Hodge conjecture asserts that, for particularly nice types of spaces called projective algebraic varieties, the pieces called Hodge cycles are actually rational linear ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...