Search Results for ""

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m,n integers and z ...

A function f is said to have a lower bound c if c<=f(x) for all x in its domain. The greatest lower bound is called the infimum.

where Gamma(z) is the gamma function and other details are discussed by Gradshteyn and Ryzhik (2000).

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

A basis, form, function, etc., in two or more variables is said to be multilinear if it is linear in each variable separately.

If m is an integer, then for every residue class r (mod m), there are infinitely many nonnegative integers n for which P(n)=r (mod m), where P(n) is the partition function P.

A function that exhibits oscillation (i.e., slope changes) is said to be oscillating, or sometimes oscillatory.