Search Results for ""

The series sum_(k=1)^inftykr^k=sum_(k=1)^inftysum_(i=k)^inftyr^i=r/((1-r)^2), valid for 0<r<1.

The theorem in set theory and logic that for all sets A and B, B=(A intersection B^_) union (B intersection A^_)<=>A=emptyset, (1) where A^_ denotes complement set of A and ...

A generalization of the p-adic norm first proposed by Kürschák in 1913. A valuation |·| on a field K is a function from K to the real numbers R such that the following ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The Hanoi graph H_n corresponding to the allowed moves in the tower of Hanoi problem. The above figure shows the Hanoi graphs for small n. The Hanoi graph H_n can be ...

g_(ij)=[0 1 0 0; 1 0 0 0; 0 0 0 -1; 0 0 -1 0]. It can be expressed as g_(ab)=l_an_b+l_bn_a-m_am^__b-m_bm^__a.

A vector field u satisfying the vector identity ux(del xu)=0 where AxB is the cross product and del xA is the curl is said to be a Beltrami field.

Euler's series transformation is a transformation that sometimes accelerates the rate of convergence for an alternating series. Given a convergent alternating series with sum ...

A connected graph is said to be highly irregular if the neighbors of each vertex have distinct vertex degrees. Highly irregular graphs exist on all orders except 3, 5 and 7, ...