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The extension ring obtained from a commutative unit ring (other than the trivial ring) when allowing division by all non-zero divisors. The ring of fractions of an integral ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

Saalschütz's theorem is the generalized hypergeometric function identity _3F_2[a,b,-n; c,1+a+b-c-n;1]=((c-a)_n(c-b)_n)/((c)_n(c-a-b)_n) (1) which holds for n a nonnegative ...

The sample variance m_2 (commonly written s^2 or sometimes s_N^2) is the second sample central moment and is defined by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ the ...

A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought ...

A simple continued fraction is a special case of a generalized continued fraction for which the partial numerators are equal to unity, i.e., a_n=1 for all n=1, 2, .... A ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it ...

A piecewise polynomial function that can have a locally very simple form, yet at the same time be globally flexible and smooth. Splines are very useful for modeling arbitrary ...

One or both of the square bracket symbols [ and ] are used in many different contexts in mathematics. 1. Square brackets are occasionally used in especially complex ...