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An independent variable is a variable whose values don't depend on changes in other variables. This is in contrast to the definition of dependent variable. As with dependent ...

Given a sequence of real numbers a_n, the infimum limit (also called the limit inferior or lower limit), written lim inf and pronounced 'lim-inf,' is the limit of ...

At the age of 17, Bernard Mares proposed the definite integral (Borwein and Bailey 2003, p. 26; Bailey et al. 2006) C_2 = int_0^inftycos(2x)product_(n=1)^(infty)cos(x/n)dx ...

A real-valued univariate function f=f(x) is said to have an infinite discontinuity at a point x_0 in its domain provided that either (or both) of the lower or upper limits of ...

Let f be a function defined on a set A and taking values in a set B. Then f is said to be an injection (or injective map, or embedding) if, whenever f(x)=f(y), it must be the ...

A function defined for all positive integers, sometimes also called an arithmetic function (Nagell 1951, p. 26) or number theoretic function (Wilf 1994, p. 58).

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

Integration under the integral sign is the use of the identity int_a^bdxint_(alpha_0)^alphaf(x,alpha)dalpha=int_(alpha_0)^alphadalphaint_a^bf(x,alpha)dx (1) to compute an ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...

The intensity measure mu of a point process X relative to a Borel set B subset R^d is defined to be the expected number of points of X falling in B. Symbolically, ...