Search Results for ""

The exsecant is a little-used trigonometric function defined by exsec(x)=secx-1, (1) where secx is the secant. The exsecant can be extended to the complex plane as ...

A distribution which arises in the study of half-integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)+1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)+1) = ...

Given a differential p-form q in the exterior algebra ^ ^pV^*, its envelope is the smallest subspace W such that q is in the subspace ^ ^pW^* subset ^ ^pV^*. Alternatively, W ...

F_x[sin(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)-e^(-2piik_0x))/(2i))dx (1) = 1/2iint_(-infty)^infty[-e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...

A system of linear differential equations (dy)/(dz)=A(z)y, (1) with A(z) an analytic n×n matrix, for which the matrix A(z) is analytic in C^_\{a_1,...,a_N} and has a pole of ...

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

Let the elements in a payoff matrix be denoted a_(ij), where the is are player A's strategies and the js are player B's strategies. Player A can get at least min_(j<=n)a_(ij) ...

Any vector field v satisfying [del ·v]_infty = 0 (1) [del xv]_infty = 0 (2) may be written as the sum of an irrotational part and a solenoidal part, v=-del phi+del xA, (3) ...