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A delta sequence is a sequence of strongly peaked functions for which lim_(n->infty)int_(-infty)^inftydelta_n(x)f(x)dx=f(0) (1) so that in the limit as n->infty, the ...
If x_1/n_1 and x_2/n_2 are the observed proportions from standard normally distributed samples with proportion of success theta, then the probability that ...
A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...
Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x, sin(2x) = 2sinxcosx (1) cos(2x) = cos^2x-sin^2x (2) = 2cos^2x-1 (3) = ...
A pair of conics obtained by expanding an equation in Monge's form z=F(x,y) in a Maclaurin series z = z(0,0)+z_1x+z_2y+1/2(z_(11)x^2+2z_(12)xy+z_(22)y^2)+... (1) = ...
The equations are x = 2/(sqrt(pi(4+pi)))(lambda-lambda_0)(1+costheta) (1) y = 2sqrt(pi/(4+pi))sintheta, (2) where theta is the solution to ...
The equations are x = ((lambda-lambda_0)(1+costheta))/(sqrt(2+pi)) (1) y = (2theta)/(sqrt(2+pi)), (2) where theta is the solution to theta+sintheta=(1+1/2pi)sinphi. (3) This ...
Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...
The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...
A generalization of the helicoid to the parametric equations x(u,v) = avcosu (1) y(u,v) = bvsinu (2) z(u,v) = cu. (3) In this parametrization, the surface has first ...
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