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The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

The second-order ordinary differential equation satisfied by the Neumann polynomials O_n(x).

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

Let M be a compact n-dimensional manifold with injectivity radius inj(M). Then Vol(M)>=(c_ninj(M))/pi, with equality iff M is isometric to the standard round sphere S^n with ...

A generalization of Schröter's formula.

Taking the locus of midpoints from a fixed point to a circle of radius r results in a circle of radius r/2. This follows trivially from r(theta) = [-x; 0]+1/2([rcostheta; ...

Any collineation from P(V) to P(V), where V is a three-dimensional vector space, is associated with a semilinear map from V to V.

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

The Jacobi symbol (a/y)=chi(y) as a number theoretic character can be extended to the Kronecker symbol (f(a)/y)=chi^*(y) so that chi^*(y)=chi(y) whenever chi(y)!=0. When y is ...