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A complex function is said to be analytic on a region R if it is complex differentiable at every point in R. The terms holomorphic function, differentiable function, and ...

A function f(x) is said to be nondecreasing on an interval I if f(b)>=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nonincreasing on an interval ...

A function f(x) is said to be nonincreasing on an interval I if f(b)<=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nondecreasing on an interval ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

A symmetric function on n variables x_1, ..., x_n is a function that is unchanged by any permutation of its variables. In most contexts, the term "symmetric function" refers ...

J_m(x)=(2x^(m-n))/(2^(m-n)Gamma(m-n))int_0^1J_n(xt)t^(n+1)(1-t^2)^(m-n-1)dt, where J_m(x) is a Bessel function of the first kind and Gamma(x) is the gamma function.

The regularized beta function is defined by I(z;a,b)=(B(z;a,b))/(B(a,b)), where B(z;a,b) is the incomplete beta function and B(a,b) is the (complete) beta function. The ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

The exponential sum function e_n(x), sometimes also denoted exp_n(x), is defined by e_n(x) = sum_(k=0)^(n)(x^k)/(k!) (1) = (e^xGamma(n+1,x))/(Gamma(n+1)), (2) where ...

A solution to the spherical Bessel differential equation. The two types of solutions are denoted j_n(x) (spherical Bessel function of the first kind) or n_n(x) (spherical ...