(mathematical analysis, statistics) Any of various real functions whose graph resembles an elongated letter "S"; specifically, the logistic function y=(eˣ)/(eˣ+1)=1/(1+e⁻ˣ).

(number theory) A function, denoted by S(n) for some positive integer n, that yields the smallest number s such that n divides the factorial s!. For example, the number 8 does not divide 1!, 2!, 3!, but does divide 4!, so S(8) = 4.

(mathematics) In harmonic analysis, any of a complete orthogonal set of functions that can be used to represent any discrete function.

(combinatorics) A Boolean function f: Z ₂ⁿ→ Z ₂ whose Walsh transform has constant absolute value.

(combinatorics) A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative.

plural of functional water

Bottled water with added vitamins, minerals, etc., sold as a health drink.

(mathematics) A function obtained from a continuous function by transfinite iteration of the operation of forming pointwise limits of sequences of functions.

(mathematics) A function in a system of differential equations that is only a function of time, unaffected by the other variables; or, more generally, any non-homogeneous source function in any variable.

plural of functional constituency