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A function whose value increases more slowly to infinity than any nonconstant polynomial is said to be a logarithmically increasing function. The prototypical example is the ...

A function f(x) decreases on an interval I if f(b)<=f(a) for all b>a, where a,b in I. If f(b)<f(a) for all b>a, the function is said to be strictly decreasing. Conversely, a ...

A function f(x) increases on an interval I if f(b)>=f(a) for all b>a, where a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. Conversely, a ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

The nth root (or "nth radical") of a quantity z is a value r such that z=r^n, and therefore is the inverse function to the taking of a power. The nth root is denoted ...

A function S_n(z) which satisfies the recurrence relation S_(n-1)(z)-S_(n+1)(z)=2S_n^'(z) together with S_1(z)=-S_0^'(z) is called a hemicylindrical function.

A Maclaurin series is a Taylor series expansion of a function about 0, (1) Maclaurin series are named after the Scottish mathematician Colin Maclaurin. The Maclaurin series ...

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

A polynomial function is a function whose values can be expressed in terms of a defining polynomial. A polynomial function of maximum degree 0 is said to be a constant ...

A function f(m) is called multiplicative if (m,m^')=1 (i.e., the statement that m and m^' are relatively prime) implies f(mm^')=f(m)f(m^') (Wilf 1994, p. 58). Examples of ...