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Poisson's equation is del ^2phi=4pirho, (1) where phi is often called a potential function and rho a density function, so the differential operator in this case is L^~=del ...

An equation derived by Kronecker: where r(n) is the sum of squares function, zeta(z) is the Riemann zeta function, eta(z) is the Dirichlet eta function, Gamma(z) is the gamma ...

The Griewank function is a function widely used to test the convergence of optimization functions. The Griewank function of order n is defined by ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

A two-dimensional generalization of the Haar transform which is used for the compression of astronomical images. The algorithm consists of dividing the 2^N×2^N image into ...

Define psi(x)={1 0<=x<1/2; -1 1/2<x<=1; 0 otherwise (1) and psi_(jk)(x)=psi(2^jx-k) (2) for j a nonnegative integer and 0<=k<=2^j-1. So, for example, the first few values of ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

The Hadamard product is a representation for the Riemann zeta function zeta(s) as a product over its nontrivial zeros rho, ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

The orthogonal polynomials defined by h_n^((alpha,beta))(x,N)=((-1)^n(N-x-n)_n(beta+x+1)_n)/(n!) ×_3F_2(-n,-x,alpha+N-x; N-x-n,-beta-x-n;1) =((-1)^n(N-n)_n(beta+1)_n)/(n!) ...