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A subset of a topological space is called clopen if it is both closed and open.

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...

The look and say sequence generated from a starting digit of 3, as given by Vardi (1991).

The cotangent function cotz is the function defined by cotz = 1/(tanz) (1) = (i(e^(iz)+e^(-iz)))/(e^(iz)-e^(-iz)) (2) = (i(e^(2iz)+1))/(e^(2iz)-1), (3) where tanz is the ...

R_m(x,y) = (J_m^'(x)Y_m^'(y)-J_m^'(y)Y_m^'(x))/(J_m(x)Y_m^'(y)-J_m^'(y)Y_m(x)) (1) S_m(x,y) = (J_m^'(x)Y_m(y)-J_m(y)Y_m^'(x))/(J_m(x)Y_m(y)-J_m(y)Y_m(x)). (2)

A special function which is given by the logarithmic derivative of the gamma function (or, depending on the definition, the logarithmic derivative of the factorial). Because ...

Given any real number theta and any positive integer N, there exist integers h and k with 0<k<=N such that |ktheta-h|<1/N. A slightly weaker form of the theorem states that ...

The quantity 12 is sometimes referred to as one dozen.

The Eisenstein units are the Eisenstein integers +/-1, +/-omega, +/-omega^2, where omega = 1/2(-1+isqrt(3)) (1) omega^2 = 1/2(-1-isqrt(3)). (2)