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For R[mu+nu]>1, int_(-pi/2)^(pi/2)cos^(mu+nu-2)thetae^(itheta(mu-nu+2xi))dtheta=(piGamma(mu+nu-1))/(2^(mu+nu-2)Gamma(mu+xi)Gamma(nu-xi)), where Gamma(z) is the gamma function.
A figurate number of the form, CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1). The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube ...
The conical spiral with angular frequency a on a cone of height h and radius r is a space curve given by the parametric equations x = (h-z)/hrcos(az) (1) y = (h-z)/hrsin(az) ...
A standard form of the linear programming problem of maximizing a linear function over a convex polyhedron is to maximize c·x subject to mx<=b and x>=0, where m is a given ...
The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...
A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...
The Euler infinity point is the intersection of the Euler line and line at infinity. Since it lies on the line at infinity, it is a point at infinity. It has triangle center ...
Euler integration was defined by Schanuel and subsequently explored by Rota, Chen, and Klain. The Euler integral of a function f:R->R (assumed to be piecewise-constant with ...
Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...
The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...
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