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Let the nth composition of a function f(x) be denoted f^((n))(x), such that f^((0))(x)=x and f^((1))(x)=f(x). Denote the composition of f and g by f degreesg(x)=f(g(x)), and ...

The integral transform defined by (Kphi)(x)=int_0^infty(x^2-t^2)_+^(lambda/2)P_nu^lambda(t/x)phi(t)dt, where y_+^alpha is the truncated power function and P_nu^lambda(x) is ...

The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x. For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for ...

If f(x,y) is an analytic function in a neighborhood of the point (x_0,y_0) (i.e., it can be expanded in a series of nonnegative integer powers of (x-x_0) and (y-y_0)), find a ...

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, ...

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 ...