Search Results for ""

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 ...

An equation for a lattice sum b_3(1) (Borwein and Bailey 2003, p. 26) b_3(1) = sum^'_(i,j,k=-infty)^infty((-1)^(i+j+k))/(sqrt(i^2+j^2+k^2)) (1) = ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

In a plane, consider a sum of N two-dimensional vectors with random orientations. Use phasor notation, and let the phase of each vector be random. Assume N unit steps are ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

The conjecture due to Pollock (1850) that every number is the sum of at most five tetrahedral numbers (Dickson 2005, p. 23; incorrectly described as "pyramidal numbers" and ...

A polynomial in which the sum of subscripts is the same in each term.

A sum over all cluster perimeters.

A number n which is an integer multiple k of the sum of its unitary divisors sigma^*(n) is called a unitary k-multiperfect number. There are no odd unitary multiperfect ...