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A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

The Abel equation of the first kind is given by y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+... (Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

Geometry which depends only on the first four of Euclid's postulates and not on the parallel postulate. Euclid himself used only the first four postulates for the first 28 ...

The absolute moment of M_n of a probability function P(x) taken about a point a is defined by M_n=int|x-a|^nP(x)dx.

A function f(x) is absolutely monotonic in the interval a<x<b if it has nonnegative derivatives of all orders in the region, i.e., f^((k))(x)>=0 (1) for a<x<b and k=0, 1, 2, ...

An abstract manifold is a manifold in the context of an abstract space with no particular embedding, or representation in mind. It is a topological space with an atlas of ...

"Abstract nonsense" is a nonderogatory term that is commonly used by mathematicians when skipping over parts of an argument that can be proven through a commonly used long ...

An abstract simplicial complex is a collection S of finite nonempty sets such that if A is an element of S, then so is every nonempty subset of A (Munkres 1993, p. 15).

An acnode, also called an isolated point or hermit point, of a curve is a point that satisfies the equation of the curve but has no neighboring points that also lie on the ...