Painlevé Property
Following the work of Fuchs in classifying first-order Ordinary Differential Equations, Painlevé studied second-order ODEs of the form
where
is Analytic in 
and rational in 
and 
. Painlevé 
found 50 types whose only movable Singularities are ordinary Poles. This characteristicis known as the Painlevé property. Six of the transcendents define new transcendents known as PainlevéTranscendents, and the remaining 44 can be integrated in terms of classical transcendents,quadratures, or the Painlevé Transcendents.See also Painlevé Transcendents- Sylvester Matrix
- Sylvester's Determinant Identity
- Sylvester's Four-Point Problem
- Sylvester's Inertia Law
- Sylvester's Line Problem
- Sylvester's Sequence
- Sylvester's Signature
- Sylvester's Triangle Problem
- Symbolic Logic
- Symmedian Line
- Symmedian Point
- Symmetric
- Symmetric Block Design
- Symmetric Design
- Symmetric Function
- Symmetric Group
- Symmetric Matrix
- Symmetric Points
- Symmetric Relation
- Symmetric Tensor
- Symmetroid
- Symmetry
- Symmetry Group
- Symmetry Operation
- Symmetry Principle