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A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

The rank of a matrix or a linear transformation is the dimension of the image of the matrix or the linear transformation, corresponding to the number of linearly independent ...

A limiting value of a holonomic function near a singular point. Holonomic constants include Apéry's constant, Catalan's constant, Pólya's random walk constants for d>2, and ...

The term "homology group" usually means a singular homology group, which is an Abelian group which partially counts the number of holes in a topological space. In particular, ...

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

A singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

When can homology classes be realized as the image of fundamental classes of manifolds? The answer is known, and singular bordism groups provide insight into this problem.