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For a discrete function f(n), the summatory function is defined by F(n)=sum_(k in D)^nf(k), where D is the domain of the function.

A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

A function composed of a set of equally spaced jumps of equal length, such as the ceiling function f(x)=[x], floor function f(x)=|_x_|, or nearest integer function f(x)=[x].

A function which has infinitely many derivatives at a point. If a function is not polygenic, it is monogenic.

Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

y=delta^'(x-a), where delta(x) is the delta function.

The prime zeta function P(s)=sum_(p)1/(p^s), (1) where the sum is taken over primes is a generalization of the Riemann zeta function zeta(s)=sum_(k=1)^infty1/(k^s), (2) where ...

F_x[1/pi(1/2Gamma)/((x-x_0)^2+(1/2Gamma)^2)](k)=e^(-2piikx_0-Gammapi|k|). This transform arises in the computation of the characteristic function of the Cauchy distribution.

A normal distribution with mean 0, P(x)=h/(sqrt(pi))e^(-h^2x^2). (1) The characteristic function is phi(t)=e^(-t^2/(4h^2)). (2) The mean, variance, skewness, and kurtosis ...

A function of more than one variable.