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The sum of the values of an integral of the "first" or "second" sort int_(x_0,y_0)^(x_1,y_1)(Pdx)/Q+...+int_(x_0,y_0)^(x_N,y_N)(Pdx)/Q=F(z) and ...

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)).

An abnormal number is a hypothetical number which can be factored into primes in more than one way. Hardy and Wright (1979) prove the fundamental theorem of arithmetic by ...

The x- (horizontal) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...

The number of data points which fall within a given class in a frequency distribution.

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, ...

A subset B of a vector space E is said to be absorbing if for any x in E, there exists a scalar lambda>0 such that x in muB for all mu in F with |mu|>=lambda, where F is the ...