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Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

Suppose that in some neighborhood of x=0, F(x)=sum_(k=0)^infty(phi(k)(-x)^k)/(k!) (1) for some function (say analytic or integrable) phi(k). Then ...

A functional differential equation is a differential equation in which the derivative y^'(t) of an unknown function y has a value at t that is related to y as a function of ...

where R[mu+nu-lambda+1]>0, R[lambda]>-1, 0<a<b, J_nu(x) is a Bessel function of the first kind, Gamma(x) is the gamma function, and _2F_1(a,b;c;x) is a hypergeometric ...

For R[mu+nu]>0, |argp|<pi/4, and a>0, where J_nu(z) is a Bessel function of the first kind, Gamma(z) is the gamma function, and _1F_1(a;b;z) is a confluent hypergeometric ...

Any entire analytic function whose range omits two points must be a constant function. Of course, an entire function that omits a single point from its range need not be a ...

The radical circle of the Stammler circles has center at the nine-point center N, which is Kimberling center X_5. The radius is given by R_S = sqrt(R^2+ON^2) (1) = ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

A function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. The space of locally integrable ...