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Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_5=f(x_5). Then Boole's rule approximating the ...

The quartic formula is a name sometimes given to one of the related explicit formulas for the four roots z_1, ..., z_4 of an arbitrary quartic equation with real coefficients ...

Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

The locus of the centers of all circumconics that also pass through the orthocenter of a triangle (which, when not degenerate, are rectangular hyperbolas) is a circle through ...

Contour integration is the process of calculating the values of a contour integral around a given contour in the complex plane. As a result of a truly amazing property of ...

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), ...

Consider a first-order logic formula Phi in Skolemized form forall x_1... forall x_nS. Then the Herbrand universe H of S is defined by the following rules. 1. All constants ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...

An apodization function given by A(x)=(21)/(50)+1/2cos((pix)/a)+2/(25)cos((2pix)/a), (1) which has full width at half maximum of 0.810957a. This function is defined so that ...

The chi distribution with n degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For n=1, the chi distribution is a ...