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Let {a_n} be a nonnegative sequence and f(x) a nonnegative integrable function. Define A_n=sum_(k=1)^na_k (1) and F(x)=int_0^xf(t)dt (2) and take p>1. For sums, ...

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_7=f(x_7). Then Hardy's rule approximating the ...

The harmonic conjugate to a given function u(x,y) is a function v(x,y) such that f(x,y)=u(x,y)+iv(x,y) is complex differentiable (i.e., satisfies the Cauchy-Riemann ...

The hat polykite is an aperiodic monotile discovered by Smith et al. (2023). It is illustrated above in an aperiodic tiling (Smith et al. 2023).

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in prolate spheroidal coordinates.

A number which is simultaneously a heptagonal number H_n and square number S_m. Such numbers exist when 1/2n(5n-3)=m^2. (1) Completing the square and rearranging gives ...

The Hermite polynomials H_n(x) are set of orthogonal polynomials over the domain (-infty,infty) with weighting function e^(-x^2), illustrated above for n=1, 2, 3, and 4. ...

Let l(x) be an nth degree polynomial with zeros at x_1, ..., x_n. Then the fundamental Hermite interpolating polynomials of the first and second kinds are defined by ...

The Herschel nonahedron is a canonical polyhedron whose skeleton is the Herschel graph. It has 11 vertices, 18 edges, and 9 faces. Of the edges, 6 are short and 12 are long. ...

A heterosquare is an n×n array of the integers from 1 to n^2 such that the rows, columns, and diagonals have different sums. (By contrast, in a magic square, they have the ...