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H_n^((2))(z)=J_n(z)-iY_n(z), (1) where J_n(z) is a Bessel function of the first kind and Y_n(z) is a Bessel function of the second kind. Hankel functions of the second kind ...

A square matrix with constant skew diagonals. In other words, a Hankel matrix is a matrix in which the (i,j)th entry depends only on the sum i+j. Such matrices are sometimes ...

An apodization function, also called the Hann function, frequently used to reduce leakage in discrete Fourier transforms. The illustrations above show the Hanning function, ...

The Harary graph H_(k,n) is a particular example of a k-connected graph with n graph vertices having the smallest possible number of edges. The smallest number of edges ...

A tiling consisting of a rhombus such that 17 rhombuses fit around a point and a second tile in the shape of six rhombuses stuck together. These two tiles can fill the plane ...

Let F(m,n) be the number of m×n (0,1)-matrices with no adjacent 1s (in either columns or rows). For n=1, 2, ..., F(n,n) is given by 2, 7, 63, 1234, ... (OEIS A006506). The ...

For a prime constellation, the Hardy-Littlewood constant for that constellation is the coefficient of the leading term of the (conjectured) asymptotic estimate of its ...

Let a_n>=0 and suppose sum_(n=1)^inftya_ne^(-an)∼1/a as a->0^+. Then sum_(n<=x)a_n∼x as x->infty. This theorem is a step in the proof of the prime number theorem, but has ...

If 0<p<infty, then the Hardy space H^p(D) is the class of functions holomorphic on the disk D and satisfying the growth condition ...

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, ...