Search Results for ""

Consider a square wave f(x) of length 2L. Over the range [0,2L], this can be written as f(x)=2[H(x/L)-H(x/L-1)]-1, (1) where H(x) is the Heaviside step function. Since ...

The Machin-like formula 1/4pi=12cot^(-1)18+8cot^(-1)57-5cot^(-1)239.

For a form Q, the generic character chi_i(Q) of Q is defined as the values of chi_i(m) where (m,2d)=1 and Q represents m: chi_1(Q), chi_2(Q), ..., chi_r(Q) (Cohn 1980, p. ...

A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

The Hilbert-Schmidt norm of a matrix A is a matrix norm defined by ||A||_(HS)=sqrt(sum_(i,j)a_(ij)^2).

A quantity which rigorously assumes the value of zero is said to be identically zero. The "identically" is used for emphasis when simply stating that a quantity is (or ...

The identric mean is defined by I(a,b)=1/e((b^b)/(a^a))^(1/(b-a)) for a>0, b>0, and a!=b. The identric mean has been investigated intensively and many remarkable inequalities ...

A Fourier series in which there are large gaps between nonzero terms a_n or b_n.

Let (X,A,mu) and (Y,B,nu) be measure spaces. A measurable rectangle is a set of the form A×B for A in A and B in B.

The normal bundle of a submanifold N in M is the vector bundle over N that consists of all pairs (x,v), where x is in N and v is a vector in the vector quotient space ...