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The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

A C^infty function is a function that is differentiable for all degrees of differentiation. For instance, f(x)=e^(2x) (left figure above) is C^infty because its nth ...

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is ...

An apodization function given by A(x)=(21)/(50)+1/2cos((pix)/a)+2/(25)cos((2pix)/a), (1) which has full width at half maximum of 0.810957a. This function is defined so that ...

A partial function is a function that is not total.

A function that arises in performance analysis of partially coherent, differentially coherent, and noncoherent communications. The generalized Marcum Q-function is defined by ...

A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], ...

Elliptic alpha functions relate the complete elliptic integrals of the first K(k_r) and second kinds E(k_r) at elliptic integral singular values k_r according to alpha(r) = ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

A zero function is a function that is almost everywhere zero. The function sometimes known as "the zero function" is the constant function with constant c=0, i.e., f(x)=0 ...