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An ordinary differential equation of the form y^('')+P(x)y^'+Q(x)y=0. (1) Such an equation has singularities for finite x=x_0 under the following conditions: (a) If either ...

Elliptic alpha functions relate the complete elliptic integrals of the first K(k_r) and second kinds E(k_r) at elliptic integral singular values k_r according to alpha(r) = ...

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

A curve which has at least multiplicity r_i-1 at each point where a given curve (having only ordinary singular points and cusps) has a multiplicity r_i is called the adjoint ...

The Jacobian of a linear net of curves of order n is a curve of order 3(n-1). It passes through all points common to all curves of the net. It is the locus of points where ...

If two algebraic plane curves with only ordinary singular points and cusps are related such that the coordinates of a point on either are rational functions of a ...

There are two types of bordism groups: bordism groups, also called cobordism groups or cobordism rings, and there are singular bordism groups. The bordism groups give a ...

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...

(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+alpha^2y=0 (1) for |x|<1. The Chebyshev differential equation has regular singular points at -1, 1, and infty. It can be solved by series ...